Linearized Theory of a Partially Cavitating Plano-Convex Hydrofoil Including the Effects of Camber and Thickness
|
|
- Simon Robinson
- 5 years ago
- Views:
Transcription
1 Linearized Theory of a Partially Cavitating Plano-Convex Hydrofoil nluding the Effets of Camber and Thikness By R. B. Wade HfORODYNAMlCS LASORA l C. -.ltor NA NSTTUTE OF TECHNOLO(.. ll l. CAUfORt-llA ST1tf T PASA CAUfODAA The linearized treatment of the flow over a partially avitating single hydrofoil having a flat pressure surfae and a irular-ar sution side is presented. The flow is treated as a two-dimensional, steady, invisid flow. Further assumptions made are those of inompressibility and irrotationality. The results obtained are ompared with experiment and generally good orrelation is found for the ranges of validity of the linearization. ntrodution THE investigation of the behavior of hydrofoils under varying degrees of avitation has been the objet of a great deal of interest. Several theoretial approahes have been developed for treating these problems both from a nonlinear and linearized point of view. From experimental observation [1 ), it has been established that the avity flow around a hydrofoil may be divided into three distint regimes: The partially avitating region, the fully avitating region, and an inherently unsteady zone onneting these two flow onfigurations. The partially avitating region is assoiated with flows where the avity length is less than the hord 1 Researh Fellow, Division of Engineering and Applied Siene California nstitute of Tehnology, Pasadena, Calif. 1 Numbers in braket.! designate Referenes at end of paper. Manusript reeived at SNAME Headquarters, November 3 1., length of the body and onsequently the avity terminates on the upper (or sution) surfae of the foil. n the fully avitating region, however, the avity ollapses downstream of the trailing edge and the entire upper surfae of the foil is enlosed within the avity. The problem of fully avitating flows past arbitrary shaped hydrofoils has been thoroughly treated by W u and Wang using nonlinear tehniques [] and by many authors using linearized methods [3]. For the ase of the partially avitating body, however, relatively few results have been published. n this region of flow where the amber and thikness of the profile play a role linearized tehniques are muh more amenable to solution than are nonlinear methods owing to the diffiulty of hoosing a suitable model for representing the flow in this latter ase. Wu [4] has worked out the ase of a partially avitating flat plate using a nonlinear method but all other solutions have been obtained using the linearized tehnique. These solutions inlude that of the Nomenlature a = sale parameter - A, B = onstant.! G lift oeffiient = _L_ pv 1 / hord length omplex funtion. = -- wm H(n H = homogeneous solution = -vr<r - 1) i integral -v= = avitation number = p., - p. pv 1 / l = Poo = avity length pressure at infinity P avity pressure p. al f. At + B rat1n omp ex unt1n = r<r _ l) R = radius u, 11 = veloity omponent.! in x, y-diretions u, v perturbation omponent.! V upstream veloity W(z) w(z) omplex veloity funtions x, y oordinate axes in physial plane z = x + iy omplex physial plane a = angle of attak p density angle subtended by tangent.! to upper foil surfae r = + i 7] at leading and trailing edges transformed omplex plane. 71 oordinate S..l:es in transformed plane Reprinted from the Journol of Ship Reseorh, Vol. 11, No. 1, pp. - 7 JOURNAL OF SHP RESEARCH
2 j--z partially avitating flat plate by Aosta [5] whih was also subsequently treated by Geurst [6]. n Geursts paper the formulation is arried out for an arbitrary profile having zero thikness. The ase of a profile inluding thikness effets has not been treated in the literature. The present paper deals with the linearized treatment of a partially avitating flow over a plano-onvex (flat pressure surfae and irular-ar sution side) hydrofoil inluding the effets of amber and profile thikness. The results so obtained are then ompared with the experimental results obtained on suh hydrofoils by several authors, viz., Balhan [7], Meijer [8), and Wade [1]. The purpose of studying suh a profile setion, a member of the arman-trefftz family of airfoils, arises from the extensive use of slight variant from this form in propeller work. Fig. 1 Partially avitating plano-onvex hydrofoil Formulation ofj Problem The hydrofoil is held at an angle of attak, a, to the free-stream veloity, V, as illustrated in Fig. 1. For the present problem it is assumed that a avity forms on the top side of the hydrofoil starting at the leading edge. The avity then terminates on the upper surfae. The angle subtended by the tangents to the irular surfae at the leading and trailing edges, n, is assumed to be small as is the angle of attak, a. These assumptions are in keeping with the linearized theory [3]. With these assumptions it is possible to onsider the veloity field as a perturbation on the free-stream veloity, V, allowing one to write the veloity at any point in the fluid as q = V(1 + u, v) = (u, v) (1) where u, v are the perturbation omponents. Furthermore the equation for the irular-ar sution surfae an be written in the form ely = (1 - x) dx The boundary onditions on the veloity funtion, within the framework of the linearized theory, then beome with the help of Bernoullis equation v = - V a + Vf! (1 - x), for the top wetted surfae v = - V a, for the bottom wetted surfae u = V ( 1 + ) on the avity surfae MARCH 1967 z - PL ANE Fig. y r dl v:-va+v dx Linearized problem in physial z-plane is the avitation number defined as where = P - P pv / P = pressure at infinity P = avity pressure These bow1dary onditions are applied along a slit representing the body in the physial plane, as illustrated in Fig.. From the initial assumptions that the flow is inompressible and irrotational, the funtion (3) W(z) = u - iv (4) is therefore an analyti funtion of the omplex varia ble z. The transformation where r = w 1 (5a) (5b) transforms the slit in the z-plane into the upper half r plane, suh that the entire real axis of the r-plane beomes the surfae of the foil. Furthermore the region < r < 1 beomes the avity surfae. With this transformation the point at infinity in the z-plane is transformed into the point ia in the r-plane as seen in Fig. 3. The relevant boundary onditions are also shown in this figure. i o (z: a> ) v : - Vo u:v(+l v =- Va +Y{! [ r-x( )] t- PLANE Fig. 3 Transform s-plane 1
3 Further onditions to be satisfied are that the veloity at infinity be equal to the free-stream veloity, V, i.e. lim W (z) = V (6) -"" and that the avity-hydrofoil system form a losed body. This requirement may be expressed as r dy = o (7) J body where y represents the ordinates of points on the bodyavity system. Furthermore, at the trailing edge, due to the finite trailing-edge angle of the hydrofoil, the veloity there must behave logarithmially. This replaes the usual utta ondition at the trailing edge. Considering the ftmtion w(z) = W(z) - V ( 1 + ) - iva in the r-plan e, we have: maginary part w = - ro < < Realpartw =O << 1 maginary part w = - VQ [1 - xw] 1 < < ro f we ontinue w(z) analytially through the interval < < 1 into the lower half plane, suh that w(r ) = - w(r ) then the real part of w is an uneven funtion of 7J and the imaginary part of w is an even funtion of 7J. We an thus formulate the following boundary-value problem in the r -plane: w+ + w- = - ro < < w+ - w- = w+ + w- =- i vn [1 - xw 1 < < 1 where the supersripts refer to the value of w(t) as 71 - ±. The problem therefore redues to a Hilbert problem the solution of whih an be found by applying the proedures given in referene [9]. Solution of the Problem Let us first onsider the homogeneous problem H + + H H+- H H + + H - - ro << < < 1 1 <<ro t an be seen that H (t) is ontinuous for < < 1 but A funtion satis has a jump for outside of this range. fying these onditions is H = vnr - 1) where we take the branh uts of H to be along the real axis outside the interval < < 1, and we further require that H,..., r We now onsider the funtion as r - ro a (r) = w(r) H (r) The boundary onditions for this funtion are w+ w - a + - a - = = (w+ + w-) j H + = H + H- w+ w- a + - a- = = (w+ - w-)j H + = H + H - w+ w- a+ - a- = = (w+ + w-)j H + H + H- - ivq [1 Wl vh - 1) - x - ro << << 1 By means of Plemeljs formula, we an express an analyti funtion in the upper half plane by its values along the entire real axis aording to the formula F(z) =!. J "" wherej(x) = j+(x) - j-(x). Aordingly, we obtain j(x) dx 7rZ - "" X - Z a ( ) _ Vn f "" 1 - x dt r - - 1r J1 vh - )C- r) " This solution represents a partiular solution of the problem; the general solution being given by w(r) = - vrr - 1) f "" 1 - x d J1 vh - 1 )(- r) + P (r) vnr - 1) where P (t) is a rational funtion of r whih an have poles only at the points =, 1. At the trailing edge, i.e., the point r = ro in the r-plane, w(r ) an at most behave logarithmially. This behavior, a onsequene of the linearized thikness effet, is already inorporated in the integral part of the solution. Hene P(r) an only be of the form Ar + B rr - 1) where A, B are real onstants. We finally get for our solution JOURNAL OF SHP RESEARCH
4 1.8 a=6 1.6 Ct r = O"o 1--- r--- 7o/o 6Yo 1-- 4"/o t-- "/o -... O"o Fig. 4 Lift oeffiient versus avitation number for various thikness ratios at a fixed angle of attak of 6 deg ( r) vnv ( 1) r 1 - x d w - 1r r r - J 1 vh - 1)( - n At+ B + -vt(t - 1) (S) where x an be obtained from the transformation equation (5a) as x = e + a The onstants A and B an be evaluated from the ondition that w (t) = v at r = ia As we will only be onerned with evaluating the foregoing integral at r = ia, we an write this integral as r Ha - e> = J V(( + a) d. r (a - ) + w J l vr- l )(e + a ) For purposes of omputation it is more onvenient to hange the limits of integration to a finite interval. By suessively substituting = 1/ t and t = 1 - x, these integrals redue to t (a t - 1). f 1 t(a t - 1) = Jo (1 + at) dx + ta Jo (1 + at) dx or =/+ ii where / and are only funtions of the parameter a. The integrals are represented in this fashion as it simplifies the numerial integration proess. t is possible to evaluate these integrals in losed form but this leads to a ompliated expression whih is not very useful. The onstants A and B an now be evaluated with the a.id of equation (6). After some manipulation we obtain A = - V ( 1 + a )!. [!f sin 1/t_ + a os!] a and B = - Val(l + a );. [!i + Vf! (1 + a ) ( sin 1/1 + / os 1/1 J 11" os 1/t_- a sin V:.J + Vr! a(l + a )1 ( os 1/1 - / sin 1/1) 11" where!f = 1r + tan- 1/ a. These,_ expressions express the onstants A and B in terms of the parameter a. The first terms in the aforementioned expressions orrespond to the flat-plate solution and the amber and thikness effets are inorporated in the seond terms. The relationship between the avitation number and the avity length l is obtained by applying the losure ondition, equation (7). This ondition may be written in the following form: MARCH
5 1. a Q = 6 CL / { t4 -t. BA LHAN MEJER. f/ "1 )(_ v op 1(. v / L // --:L: 6. / j " --!L". 4. / Y.. e Fig. 5 Ratio of avitation number to twie angle of attak as a funtion of avity length-to-hord ratio for various thikness ratios at a fixed angle of attak of 6 deg Fig. 6 Comparison of theoretial lift oeffiient with experimental results for a 4-perent-thik plano-onvex hydrofoil as a funtion of avitation number for various angles of attak or f dy= f vdx=o J body J body m f W(r) ddz ds = J body where m denotes the imaginary part of the integral. We are furthermore interested in the lift on the body. Within the limitations of the linearized theory this is given by or s CL = - f udx V J body CL = - Re f W(s) dz ds V J body ds where Re denotes the real part of the integral. Sine the body is now the entire real axis in the s-plane, we have to evaluate the integral where 4 = J-" W(s) dzd ds +m S dz a s ds <r - ia)(s + ia) (9) Sine dz _,... 1 asr - ds s 3 there is no ontribution to t he integral by ompleting the ontour by a large irle R and letting R - ro. The value of the integral is then given by the residue of the integrand at the double pole s = ia. Sine the integral traverses the body in a ounter-lokwise fashion in the z-plane whih orresponds to a lokwise sense in the s-plane, we have whih redues to ro = -7Ti[Residue at s = ia] = - 7ra [dwj ds r=ia (1) Carrying out the indiated proedure and separating the result into real and imaginary parts we obtain, after onsiderable algebra, the following expressions for the losure ondition and for the lift oeffiient, C L: 1rA 3.J; ---.,-----,.,. os - Va1(1 + a )1 + 1rB [. 3,Y +. 3,YJ Va1(1 + a)1 SD a SD + JOURNAL OF SHP RESEARCH
6 o a < t = 4t lj,, 1: /l /J a.. /,1 t tl t/..._ 4 _,/// :- " ME JER o.a 1. Fig. 7 Some avity-length measurements ompared with the theory for a 4-perent-thik plano-onvex hydrofoil at various angles of anak g CL.. a o.a.6.4 f 7,.. f/. lk. y a s!q v. / fv / // v/6 f /6 r--- L /) 4 lg( v z WADE a -. a 6 1 o Fig. 8 Comparison of theoretial lift oeffiient with experimental results for a 7-perent-thik plano-onvex hydrofoil as a funtion of avitation number for various angles of anak! and where 1 )/ [11 ( sin f + a os!) 4 a 1 + a -! ( os - a sin ) J +, 1 ( = 4 i ( t ta(at - 1) dx 4 Jo (1 + at)3 From the e results the graphs shown in Figs. 4-1 were obtained. The omputations were arried out on a BM 794 omputer. The range of values investigated was for angles of attak from to 1 deg and values of Q orrespondjng to thikness ratios of from to 1 perent. Disussion Figs. 4 and 5 show t he effet of profile ontour on the performane of the hydrofoil under partially avitating onditions. Only urves for one angle of attak, a = 6 deg, are shown. t is een that the effets of amber and thikness are to inrease lift at any given ayjtation number with a orresponding inrease in avity length. n the linearized theory the validity of the results is usually re trited to a ertain range of ayjtation numbers due to the type of avity losure used. For the present ase this range of validity holds for values of avity length-to-hord ratio less than about.75, the same value as for the flat-plate ase [3, 4]. This is apparent from Fig. 5 where it is seen that the avitation number reahes a minimum value at this point. Values outside t his range would give rise to the possibility of two avity lengths for any given ayjtation number. t should be noted that the foregoing alulations are MARCH
7 a u l t a a = WADE 4. 6 a to : / - / 4 /, /7 - e - / A L Fig. 9 Some avity-length measurements ompared with theor y for a 7-per ent-thik plano-onvex hydrofoil at various angles of attak a <.3 : jl 1 1!,. 7t. CORRECTED TH EORY fy : -,... t-,,.,, 6.,, _ _ e -..A _... _ to WADE e to Fig. 1 Comparison of experimental avity-length m easurements with orreted theory for a 7-perent-thik hydrofoil at various angles of attak based on the assumption that the avity springs from the leading edge at all times. Under ertain onfigurations of angle of attak and thikness ratio this assumption may not be physially possible, as brought out by the findings of experimental investigation [1], vhere at lower angles of attak a avity starts downstream of the leading edge at approximately the point of maximum thikness. This should therefore be kept in mind when applying the aforementioned results. t may be noted that the fully wetted results obtained from this linearized theory for a hydrofoil of 7 perent thikness ratio give a zero lift angle of attak of -4 deg with a orresponding lift oeffiient at zero angle of attak of.438. This ompares with values of -4 deg 1 min and.479 obtained by onformal mapping tehniques, and with -4 deg and.38 obtained from experiment [1]. n Figs. 6 to 1 a omparison of the theoretial results is shown with points obtained from various experimental investigations. Fig. 6 illustrates the lift oeffiients for a 4-perent-thik plano-onvex hydrofoil as obtained by Balhan and Meijer. t will be seen that good agreement is found between experiment and theory. Fig. 7 ompares some avity-length measurements obtained by Meijer with those predited by the present theory. Here the agreement is not as good. The disrepany in this ase may be partly due to the 6 diffiulty in measuring avity lengths under these irumstanes owing to a ertain arbitrariness in interpreting where the avity ends. However, a more likely explanation is the fat that in Meijers experiments the avitation numbers are based on vapor pressure and not on measured avity pressure. t is well known that the avitation number is dereased if measured avity pressure is used in determining this parameter. This lowering would t herefore tend to improve the orrelation between experiment and theory. n Fig. 8 omparison is made between experiment and theory for a 7-perent-thik hydrofoil. Here it will be seen that the experimental results are between to 3 perent lower than the theoretial values-the larger value orresponding to the largest angle of attak. This disrepany is probably due to the deterioration of the linearization at these higher thiknesses in onjuntion with the inreasing angle of attak. The orresponding avity lengths are shown in Fig. 9 where again a similar disrepany exists. t is knmvn from airfoil experiments that if the theoretial lift is arbitrarily adjusted to the experimental value, t he theoretial pressure distribution on the foil agrees on the whole with the experimental one. This artifie ahieves two purposes. First, it endeavors to some extent to aount for real fluid effets and seond, it affords a means of heking whether the experimental JOURNAL OF SHP RESEARCH
8 data are self-onsistent. This approah was utilized here. The theoretial lift oeffiient was adjusted to the experimental value for the same avity lengths and the orresponding theoretial avitation number was altered aordingly. These adjusted avitation numbers are shown plotted in Fig. 1. t is seen that the orreted theoreti<ial values are in good agreement with the experimental points. The..: limiting ase when the thikness of the hydrofoil is "teo redues in the limit to that of the performane of a partially avitating flat plate. Conlusion n onlusion it may be stated that the linearized theory presented predits with suffiient auray the performane of a partially avitating plano-onvex hydrofoil having perentage thiknesses up to 5 perent. For larger thiknesses the linearization breaks down and for 7 perent thikness ratios overestimates the lift oeffiients by to 3 perent, for angles of attak up to 1 deg. The limiting ases of a flat plate and a fully wetted plano-onvex hydrofoil are retrieved by taking the appropriate limits. Aknowledgments The author wishes to thank Dr. A. J. Aosta for his onstant interest and many helpful disussions. This work was supported by the Department of the Navy under Contrat Nonr (4). Referenes 1 R. B. Wade and A. J. Aosta, "Experimental Observations on the Flow Past a Plano-Convex Hydrofoil," Trans. ASME, Journal of Basi Engineering, Paper presented June 7, 1965, Applied Mehanis/ Fluids Engineering Conferene, Washington, D. C. T. Yao-Tsu Wu and D. P. Wang, "A Wake Model for Free Streamline Flow Theory, Part, Cavity Flows Past Obstales of Arbitrary Profile," J ournal of Fluid Mehanis, vol. 18, part 1, 1964, pp B. R. Parkin, "Linearized Theory of Cavity Flow in Two Din1ensions," Rand Corporation Report P-1745, T. Yao-Tsu Wu, "A Wake Model for Free-Streamline Flow Theory, Part 1, Fully and Partially Developed Wake Flows and Cavity Flows Past an Oblique Flat Plate," J ournal of Fluid Mehanis, vol. 13, part, 196, pp A. J. Aosta, "A Note on Partial Cavitation of Flat Plate Hydrofoils," California nstitute of Tehnology Hydrodynamis Laboratory Report No. E-19.9, J. A. Geurst, "Linearized Theory for Partially Cavitated Hydrofoils," nternational Shipbuilding Progress, vol. 6, no. 6, J. Balban, "Metingen aan Enige bij Sheepshroenen Gebruikelijke Profielen in Vlokke Stroming met en Zonder Cavitie," Ned. Sheepsbouwkundig Proefstation te Wageningen, M. C. 1lleijer, "Some Experiments on Partially Cavitating Hydrofoils," nternational Shipbuilding Progress, vol. 6, no. 6, N.. u skbelisbvili, Singular ntegral Equations, P. Noordboff, Limited, Groningen, Holland, MARCH
Chapter 3 Lecture 7. Drag polar 2. Topics. Chapter-3
hapter 3 eture 7 Drag polar Topis 3..3 Summary of lift oeffiient, drag oeffiient, pithing moment oeffiient, entre of pressure and aerodynami entre of an airfoil 3..4 Examples of pressure oeffiient distributions
More informationCavity flow with surface tension past a flat plate
Proeedings of the 7 th International Symposium on Cavitation CAV9 Paper No. ## August 7-, 9, Ann Arbor, Mihigan, USA Cavity flow with surfae tension past a flat plate Yuriy Savhenko Institute of Hydromehanis
More informationMillennium Relativity Acceleration Composition. The Relativistic Relationship between Acceleration and Uniform Motion
Millennium Relativity Aeleration Composition he Relativisti Relationship between Aeleration and niform Motion Copyright 003 Joseph A. Rybzyk Abstrat he relativisti priniples developed throughout the six
More informationThe Hanging Chain. John McCuan. January 19, 2006
The Hanging Chain John MCuan January 19, 2006 1 Introdution We onsider a hain of length L attahed to two points (a, u a and (b, u b in the plane. It is assumed that the hain hangs in the plane under a
More informationEFFECTS OF COUPLE STRESSES ON PURE SQUEEZE EHL MOTION OF CIRCULAR CONTACTS
-Tehnial Note- EFFECTS OF COUPLE STRESSES ON PURE SQUEEZE EHL MOTION OF CIRCULAR CONTACTS H.-M. Chu * W.-L. Li ** Department of Mehanial Engineering Yung-Ta Institute of Tehnology & Commere Ping-Tung,
More informationA Heuristic Approach for Design and Calculation of Pressure Distribution over Naca 4 Digit Airfoil
IOSR Journal of Engineering (IOSRJEN) ISSN (e): 2250-3021, ISSN (p): 2278-8719 PP 11-15 www.iosrjen.org A Heuristi Approah for Design and Calulation of Pressure Distribution over Naa 4 Digit Airfoil G.
More information2. The Energy Principle in Open Channel Flows
. The Energy Priniple in Open Channel Flows. Basi Energy Equation In the one-dimensional analysis of steady open-hannel flow, the energy equation in the form of Bernoulli equation is used. Aording to this
More informationEffects of Vane Sweep on Fan-Wake/Outlet-Guide-Vane Interaction Broadband Noise
Effets of Vane Sweep on Fan-Wake/Outlet-Guide-Vane Interation Broadband Noise Hongbin Ju* GE Global Researh Center, One Researh Cirle, Niskayuna, NY. 09 A method is developed for prediting broadband noise
More informationComplexity of Regularization RBF Networks
Complexity of Regularization RBF Networks Mark A Kon Department of Mathematis and Statistis Boston University Boston, MA 02215 mkon@buedu Leszek Plaskota Institute of Applied Mathematis University of Warsaw
More informationWhere as discussed previously we interpret solutions to this partial differential equation in the weak sense: b
Consider the pure initial value problem for a homogeneous system of onservation laws with no soure terms in one spae dimension: Where as disussed previously we interpret solutions to this partial differential
More information3 Tidal systems modelling: ASMITA model
3 Tidal systems modelling: ASMITA model 3.1 Introdution For many pratial appliations, simulation and predition of oastal behaviour (morphologial development of shorefae, beahes and dunes) at a ertain level
More informationThe gravitational phenomena without the curved spacetime
The gravitational phenomena without the urved spaetime Mirosław J. Kubiak Abstrat: In this paper was presented a desription of the gravitational phenomena in the new medium, different than the urved spaetime,
More informationNUMERICAL SIMULATION OF ATOMIZATION WITH ADAPTIVE JET REFINEMENT
Paper ID ILASS8--7 ILASS 28 Sep. 8-, 28, Como Lake, Italy A44 NUMERICAL SIMULATION OF ATOMIZATION WITH ADAPTIVE JET REFINEMENT Anne Bagué, Daniel Fuster, Stéphane Popinet + & Stéphane Zaleski Université
More informationDetermination of the Aerodynamic Characteristics of Flying Vehicles Using Method Large Eddy Simulation with Software ANSYS
Automation, Control and Intelligent Systems 15; 3(6): 118-13 Published online Deember, 15 (http://www.sienepublishinggroup.om//ais) doi: 1.11648/.ais.1536.14 ISSN: 38-5583 (Print); ISSN: 38-5591 (Online)
More information13.Prandtl-Meyer Expansion Flow
3.Prandtl-eyer Expansion Flow This hapter will treat flow over a expansive orner, i.e., one that turns the flow outward. But before we onsider expansion flow, we will return to onsider the details of the
More informationHankel Optimal Model Order Reduction 1
Massahusetts Institute of Tehnology Department of Eletrial Engineering and Computer Siene 6.245: MULTIVARIABLE CONTROL SYSTEMS by A. Megretski Hankel Optimal Model Order Redution 1 This leture overs both
More informationELECTROMAGNETIC NORMAL MODES AND DISPERSION FORCES.
ELECTROMAGNETIC NORMAL MODES AND DISPERSION FORCES. All systems with interation of some type have normal modes. One may desribe them as solutions in absene of soures; they are exitations of the system
More informationModeling of Threading Dislocation Density Reduction in Heteroepitaxial Layers
A. E. Romanov et al.: Threading Disloation Density Redution in Layers (II) 33 phys. stat. sol. (b) 99, 33 (997) Subjet lassifiation: 6.72.C; 68.55.Ln; S5.; S5.2; S7.; S7.2 Modeling of Threading Disloation
More informationNon-Markovian study of the relativistic magnetic-dipole spontaneous emission process of hydrogen-like atoms
NSTTUTE OF PHYSCS PUBLSHNG JOURNAL OF PHYSCS B: ATOMC, MOLECULAR AND OPTCAL PHYSCS J. Phys. B: At. Mol. Opt. Phys. 39 ) 7 85 doi:.88/953-75/39/8/ Non-Markovian study of the relativisti magneti-dipole spontaneous
More informationTHE REFRACTION OF LIGHT IN STATIONARY AND MOVING REFRACTIVE MEDIA
HDRONIC JOURNL 24, 113-129 (2001) THE REFRCTION OF LIGHT IN STTIONRY ND MOVING REFRCTIVE MEDI C. K. Thornhill 39 Crofton Road Orpington, Kent, BR6 8E United Kingdom Reeived Deember 10, 2000 Revised: Marh
More informationINTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 2, No 4, 2012
INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume, No 4, 01 Copyright 010 All rights reserved Integrated Publishing servies Researh artile ISSN 0976 4399 Strutural Modelling of Stability
More informationThe Second Postulate of Euclid and the Hyperbolic Geometry
1 The Seond Postulate of Eulid and the Hyperboli Geometry Yuriy N. Zayko Department of Applied Informatis, Faulty of Publi Administration, Russian Presidential Aademy of National Eonomy and Publi Administration,
More informationIntegral Solution for the Mean Flow Profiles of Turbulent Jets, Plumes, and Wakes
Amit Agrawal e-mail: agrawaa@me.udel.edu Ajay K. Prasad e-mail: prasad@me.udel.edu Department of Mehanial Engineering, University of Delaware, Newark, DE 19716 Integral Solution for the Mean Flow Profiles
More informationDepartment of Mechanical Engineering
Department o Mehanial Engineering AMEE41 / ATO4 Aerodynamis Instrutor: Marios M. Fyrillas Email: eng.m@it.a.y Homework Assignment #4 QESTION 1 Consider the boundary layer low on a lat plate o width b (shown
More informationEffect of Different Types of Promoters on Bed Expansion in a Gas-Solid Fluidized Bed with Varying Distributor Open Areas
Journal of Chemial Engineering of Japan, Vol. 35, No. 7, pp. 681 686, 2002 Short Communiation Effet of Different Types of Promoters on Bed Expansion in a Gas-Solid Fluidized Bed with Varying Distributor
More informationDevelopment of Fuzzy Extreme Value Theory. Populations
Applied Mathematial Sienes, Vol. 6, 0, no. 7, 58 5834 Development of Fuzzy Extreme Value Theory Control Charts Using α -uts for Sewed Populations Rungsarit Intaramo Department of Mathematis, Faulty of
More informationCritical Reflections on the Hafele and Keating Experiment
Critial Refletions on the Hafele and Keating Experiment W.Nawrot In 1971 Hafele and Keating performed their famous experiment whih onfirmed the time dilation predited by SRT by use of marosopi loks. As
More informationAnalysis of discretization in the direct simulation Monte Carlo
PHYSICS OF FLUIDS VOLUME 1, UMBER 1 OCTOBER Analysis of disretization in the diret simulation Monte Carlo iolas G. Hadjionstantinou a) Department of Mehanial Engineering, Massahusetts Institute of Tehnology,
More informationA simple expression for radial distribution functions of pure fluids and mixtures
A simple expression for radial distribution funtions of pure fluids and mixtures Enrio Matteoli a) Istituto di Chimia Quantistia ed Energetia Moleolare, CNR, Via Risorgimento, 35, 56126 Pisa, Italy G.
More informationPhysical Laws, Absolutes, Relative Absolutes and Relativistic Time Phenomena
Page 1 of 10 Physial Laws, Absolutes, Relative Absolutes and Relativisti Time Phenomena Antonio Ruggeri modexp@iafria.om Sine in the field of knowledge we deal with absolutes, there are absolute laws that
More informationRobust Flight Control Design for a Turn Coordination System with Parameter Uncertainties
Amerian Journal of Applied Sienes 4 (7): 496-501, 007 ISSN 1546-939 007 Siene Publiations Robust Flight ontrol Design for a urn oordination System with Parameter Unertainties 1 Ari Legowo and Hiroshi Okubo
More informationBeams on Elastic Foundation
Professor Terje Haukaas University of British Columbia, Vanouver www.inrisk.ub.a Beams on Elasti Foundation Beams on elasti foundation, suh as that in Figure 1, appear in building foundations, floating
More informationLecture 3 - Lorentz Transformations
Leture - Lorentz Transformations A Puzzle... Example A ruler is positioned perpendiular to a wall. A stik of length L flies by at speed v. It travels in front of the ruler, so that it obsures part of the
More informationINFLUENCE OF OPERATING AND CONSTRUCTION PARAMETERS ON THE BEHAVIOR OF HYDRAULIC CYLINDER SUBJECTED TO JERKY MOTION
Proeedings of ICFDP 8: 8 th International Congress of Fluid Dynamis & Propulsion Deember 14-17, 006, Sharm El-Shiekh, Sinai, Egypt ICFDP8-EG-154 INFLUENCE OF OPERATING AND CONSTRUCTION PARAMETERS ON THE
More informationCalculation of Desorption Parameters for Mg/Si(111) System
e-journal of Surfae Siene and Nanotehnology 29 August 2009 e-j. Surf. Si. Nanoteh. Vol. 7 (2009) 816-820 Conferene - JSSS-8 - Calulation of Desorption Parameters for Mg/Si(111) System S. A. Dotsenko, N.
More informationA model for measurement of the states in a coupled-dot qubit
A model for measurement of the states in a oupled-dot qubit H B Sun and H M Wiseman Centre for Quantum Computer Tehnology Centre for Quantum Dynamis Griffith University Brisbane 4 QLD Australia E-mail:
More informationChapter 2 Linear Elastic Fracture Mechanics
Chapter 2 Linear Elasti Frature Mehanis 2.1 Introdution Beginning with the fabriation of stone-age axes, instint and experiene about the strength of various materials (as well as appearane, ost, availability
More informationDIGITAL DISTANCE RELAYING SCHEME FOR PARALLEL TRANSMISSION LINES DURING INTER-CIRCUIT FAULTS
CHAPTER 4 DIGITAL DISTANCE RELAYING SCHEME FOR PARALLEL TRANSMISSION LINES DURING INTER-CIRCUIT FAULTS 4.1 INTRODUCTION Around the world, environmental and ost onsiousness are foring utilities to install
More informationControl Theory association of mathematics and engineering
Control Theory assoiation of mathematis and engineering Wojieh Mitkowski Krzysztof Oprzedkiewiz Department of Automatis AGH Univ. of Siene & Tehnology, Craow, Poland, Abstrat In this paper a methodology
More informationIMPEDANCE EFFECTS OF LEFT TURNERS FROM THE MAJOR STREET AT A TWSC INTERSECTION
09-1289 Citation: Brilon, W. (2009): Impedane Effets of Left Turners from the Major Street at A TWSC Intersetion. Transportation Researh Reord Nr. 2130, pp. 2-8 IMPEDANCE EFFECTS OF LEFT TURNERS FROM THE
More informationA EUCLIDEAN ALTERNATIVE TO MINKOWSKI SPACETIME DIAGRAM.
A EUCLIDEAN ALTERNATIVE TO MINKOWSKI SPACETIME DIAGRAM. S. Kanagaraj Eulidean Relativity s.kana.raj@gmail.om (1 August 009) Abstrat By re-interpreting the speial relativity (SR) postulates based on Eulidean
More informationThin Airfoil Theory Lab
Thin Airfoil Theory Lab AME 3333 University of Notre Dame Spring 26 Written by Chris Kelley and Grady Crahan Deember, 28 Updated by Brian Neiswander and Ryan Kelly February 6, 24 Updated by Kyle Heintz
More informationTheory. Coupled Rooms
Theory of Coupled Rooms For: nternal only Report No.: R/50/TCR Prepared by:. N. taey B.., MO Otober 00 .00 Objet.. The objet of this doument is present the theory alulations to estimate the reverberant
More informationLecture Notes 4 MORE DYNAMICS OF NEWTONIAN COSMOLOGY
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physis Department Physis 8.286: The Early Universe Otober 1, 218 Prof. Alan Guth Leture Notes 4 MORE DYNAMICS OF NEWTONIAN COSMOLOGY THE AGE OF A FLAT UNIVERSE: We
More informationAverage Rate Speed Scaling
Average Rate Speed Saling Nikhil Bansal David P. Bunde Ho-Leung Chan Kirk Pruhs May 2, 2008 Abstrat Speed saling is a power management tehnique that involves dynamially hanging the speed of a proessor.
More informationThe universal model of error of active power measuring channel
7 th Symposium EKO TC 4 3 rd Symposium EKO TC 9 and 5 th WADC Workshop nstrumentation for the CT Era Sept. 8-2 Kosie Slovakia The universal model of error of ative power measuring hannel Boris Stogny Evgeny
More informationSTUDY OF INHERENT FREQUENCY OF HELMHOLTZ RESONATOR
005 WJTA Amerian Waterjet Conferene August -3, 005! Houston, Texas Paper 6B-4 STUDY OF INHERENT FREQUENCY OF HELMHOLT RESONATOR Gong Weili An Liqian Cui Longlian Xie Guixin Shool of Mehanis, Arhiteture
More informationMinimum Specific Energy and Critical Flow Conditions in Open Channels
Minimum Speifi Energy and Critial Flow Conditions in Open Channels H. Chanson Abstrat: In open hannels, the relationship between the speifi energy and the flow depth exhibits a minimum, and the orresponding
More informationarxiv:gr-qc/ v2 6 Feb 2004
Hubble Red Shift and the Anomalous Aeleration of Pioneer 0 and arxiv:gr-q/0402024v2 6 Feb 2004 Kostadin Trenčevski Faulty of Natural Sienes and Mathematis, P.O.Box 62, 000 Skopje, Maedonia Abstrat It this
More informationEE 321 Project Spring 2018
EE 21 Projet Spring 2018 This ourse projet is intended to be an individual effort projet. The student is required to omplete the work individually, without help from anyone else. (The student may, however,
More informationRESEARCH ON RANDOM FOURIER WAVE-NUMBER SPECTRUM OF FLUCTUATING WIND SPEED
The Seventh Asia-Paifi Conferene on Wind Engineering, November 8-1, 9, Taipei, Taiwan RESEARCH ON RANDOM FORIER WAVE-NMBER SPECTRM OF FLCTATING WIND SPEED Qi Yan 1, Jie Li 1 Ph D. andidate, Department
More informationOn Certain Singular Integral Equations Arising in the Analysis of Wellbore Recharge in Anisotropic Formations
On Certain Singular Integral Equations Arising in the Analysis of Wellbore Reharge in Anisotropi Formations C. Atkinson a, E. Sarris b, E. Gravanis b, P. Papanastasiou a Department of Mathematis, Imperial
More informationEXPERIMENTAL STUDY ON BOTTOM BOUNDARY LAYER BENEATH SOLITARY WAVE
VOL. 11, NO. 8, APRIL 16 ISSN 1819-668 6-16 Asian Researh Publishing Network (ARPN). All rights reserved. EXPERIMENTAL STUDY ON BOTTOM BOUNDARY LAYER BENEATH SOLITARY WAVE Bambang Winarta 1, Nadiatul Adilah
More informationCRITICAL EXPONENTS TAKING INTO ACCOUNT DYNAMIC SCALING FOR ADSORPTION ON SMALL-SIZE ONE-DIMENSIONAL CLUSTERS
Russian Physis Journal, Vol. 48, No. 8, 5 CRITICAL EXPONENTS TAKING INTO ACCOUNT DYNAMIC SCALING FOR ADSORPTION ON SMALL-SIZE ONE-DIMENSIONAL CLUSTERS A. N. Taskin, V. N. Udodov, and A. I. Potekaev UDC
More informationNuclear Shell Structure Evolution Theory
Nulear Shell Struture Evolution Theory Zhengda Wang (1) Xiaobin Wang () Xiaodong Zhang () Xiaohun Wang () (1) Institute of Modern physis Chinese Aademy of SienesLan Zhou P. R. China 70000 () Seagate Tehnology
More informationMODELLING THE POSTPEAK STRESS DISPLACEMENT RELATIONSHIP OF CONCRETE IN UNIAXIAL COMPRESSION
VIII International Conferene on Frature Mehanis of Conrete and Conrete Strutures FraMCoS-8 J.G.M. Van Mier, G. Ruiz, C. Andrade, R.C. Yu and X.X. Zhang Eds) MODELLING THE POSTPEAK STRESS DISPLACEMENT RELATIONSHIP
More informationFour-dimensional equation of motion for viscous compressible substance with regard to the acceleration field, pressure field and dissipation field
Four-dimensional equation of motion for visous ompressible substane with regard to the aeleration field, pressure field and dissipation field Sergey G. Fedosin PO box 6488, Sviazeva str. -79, Perm, Russia
More informationNonreversibility of Multiple Unicast Networks
Nonreversibility of Multiple Uniast Networks Randall Dougherty and Kenneth Zeger September 27, 2005 Abstrat We prove that for any finite direted ayli network, there exists a orresponding multiple uniast
More informationJohn Vanderkooy Audio Research Group, Department of Physics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
An analyti seondary soure model of edge diffration impulse responses U. Peter Svensson a) and Roger I. Fred b) Department of Applied Aoustis, Chalmers University of Tehnology, SE-42 96 Göteborg, Sweden
More informationThe Electromagnetic Radiation and Gravity
International Journal of Theoretial and Mathematial Physis 016, 6(3): 93-98 DOI: 10.593/j.ijtmp.0160603.01 The Eletromagneti Radiation and Gravity Bratianu Daniel Str. Teiului Nr. 16, Ploiesti, Romania
More informationAdvanced Computational Fluid Dynamics AA215A Lecture 4
Advaned Computational Fluid Dynamis AA5A Leture 4 Antony Jameson Winter Quarter,, Stanford, CA Abstrat Leture 4 overs analysis of the equations of gas dynamis Contents Analysis of the equations of gas
More informationNew Potential of the. Positron-Emission Tomography
International Journal of Modern Physis and Appliation 6; 3(: 39- http://www.aasit.org/journal/ijmpa ISSN: 375-387 New Potential of the Positron-Emission Tomography Andrey N. olobuev, Eugene S. Petrov,
More informationFracture analysis of a functionally graded interfacial zone between two dissimilar homogeneous materials
540 Siene in China Series G: Physis, Mehanis & Astronomy 006 Vol.49 No.5 540 55 DOI: 0.007/s433-006-004-0 Frature analysis of a funtionally graded interfaial zone between two dissimilar homogeneous materials
More informationSupporting Information for
Eletroni Supplementary Material (ESI) for Nanosale This journal is The Royal Soiety of Chemistry 013 Supporting Information for Exitation polarization modulation in loalization mirosopy allows to resolve
More informationOrthogonal Complement Based Divide-and-Conquer Algorithm (O-DCA) for Constrained Multibody Systems
Orthogonal Complement Based Divide-and-Conquer Algorithm (O-DCA) for Constrained Multibody Systems Rudranarayan M. Mukherjee, Kurt S. Anderson Computational Dynamis Laboratory Department of Mehanial Aerospae
More informationMetric of Universe The Causes of Red Shift.
Metri of Universe The Causes of Red Shift. ELKIN IGOR. ielkin@yande.ru Annotation Poinare and Einstein supposed that it is pratially impossible to determine one-way speed of light, that s why speed of
More informationEvaluation of effect of blade internal modes on sensitivity of Advanced LIGO
Evaluation of effet of blade internal modes on sensitivity of Advaned LIGO T0074-00-R Norna A Robertson 5 th Otober 00. Introdution The urrent model used to estimate the isolation ahieved by the quadruple
More informationA Spatiotemporal Approach to Passive Sound Source Localization
A Spatiotemporal Approah Passive Sound Soure Loalization Pasi Pertilä, Mikko Parviainen, Teemu Korhonen and Ari Visa Institute of Signal Proessing Tampere University of Tehnology, P.O.Box 553, FIN-330,
More informationCombined Electric and Magnetic Dipoles for Mesoband Radiation, Part 2
Sensor and Simulation Notes Note 53 3 May 8 Combined Eletri and Magneti Dipoles for Mesoband Radiation, Part Carl E. Baum University of New Mexio Department of Eletrial and Computer Engineering Albuquerque
More informationTHEORETICAL PROBLEM No. 3 WHY ARE STARS SO LARGE?
THEORETICAL PROBLEM No. 3 WHY ARE STARS SO LARGE? The stars are spheres of hot gas. Most of them shine beause they are fusing hydrogen into helium in their entral parts. In this problem we use onepts of
More informationF = F x x + F y. y + F z
ECTION 6: etor Calulus MATH20411 You met vetors in the first year. etor alulus is essentially alulus on vetors. We will need to differentiate vetors and perform integrals involving vetors. In partiular,
More informationOptimization of Statistical Decisions for Age Replacement Problems via a New Pivotal Quantity Averaging Approach
Amerian Journal of heoretial and Applied tatistis 6; 5(-): -8 Published online January 7, 6 (http://www.sienepublishinggroup.om/j/ajtas) doi:.648/j.ajtas.s.65.4 IN: 36-8999 (Print); IN: 36-96 (Online)
More informationEXACT TRAVELLING WAVE SOLUTIONS FOR THE GENERALIZED KURAMOTO-SIVASHINSKY EQUATION
Journal of Mathematial Sienes: Advanes and Appliations Volume 3, 05, Pages -3 EXACT TRAVELLING WAVE SOLUTIONS FOR THE GENERALIZED KURAMOTO-SIVASHINSKY EQUATION JIAN YANG, XIAOJUAN LU and SHENGQIANG TANG
More informationA numerical Study on the Acoustic Characteristics of a Centrifugal Impeller with a Splitter
GESTS Int l Trans. Computer Siene and Engr., Vol.2, No.1 17 A numerial Study on the Aousti Charateristis of a Centrifugal Impeller with a Splitter Wan-Ho Jeon 1 1 Tehnial Researh Lab., CEDIC Ltd., #113,
More informationarxiv:cond-mat/ v1 [cond-mat.stat-mech] 16 Aug 2004
Computational omplexity and fundamental limitations to fermioni quantum Monte Carlo simulations arxiv:ond-mat/0408370v1 [ond-mat.stat-meh] 16 Aug 2004 Matthias Troyer, 1 Uwe-Jens Wiese 2 1 Theoretishe
More informationFinite-time stabilization of chaotic gyros based on a homogeneous supertwisting-like algorithm
OP Conferene Series: Materials Siene Engineering PAPER OPEN ACCESS Finite-time stabilization of haoti gyros based on a homogeneous supertwisting-like algorithm To ite this artile: Pitha Khamsuwan et al
More informationGreen s function for the wave equation
Green s funtion for the wave equation Non-relativisti ase January 2019 1 The wave equations In the Lorentz Gauge, the wave equations for the potentials are (Notes 1 eqns 43 and 44): 1 2 A 2 2 2 A = µ 0
More informationMean Activity Coefficients of Peroxodisulfates in Saturated Solutions of the Conversion System 2NH 4. H 2 O at 20 C and 30 C
Mean Ativity Coeffiients of Peroxodisulfates in Saturated Solutions of the Conversion System NH 4 Na S O 8 H O at 0 C and 0 C Jan Balej Heřmanova 5, 170 00 Prague 7, Czeh Republi balejan@seznam.z Abstrat:
More informationDetermination of the reaction order
5/7/07 A quote of the wee (or amel of the wee): Apply yourself. Get all the eduation you an, but then... do something. Don't just stand there, mae it happen. Lee Iaoa Physial Chemistry GTM/5 reation order
More informationCALCULATION OF NONLINEAR TUNE SHIFT USING BEAM POSITION MEASUREMENT RESULTS
International Journal of Modern Physis A Vol. 24, No. 5 (2009) 974 986 World Sientifi Publishing Company CALCULATION OF NONLINEAR TUNE SHIFT USING BEAM POSITION MEASUREMENT RESULTS PAVEL SNOPOK, MARTIN
More informationHeat exchangers: Heat exchanger types:
Heat exhangers: he proess of heat exhange between two fluids that are at different temperatures and separated by a solid wall ours in many engineering appliations. he devie used to implement this exhange
More informationSimplified Buckling Analysis of Skeletal Structures
Simplified Bukling Analysis of Skeletal Strutures B.A. Izzuddin 1 ABSRAC A simplified approah is proposed for bukling analysis of skeletal strutures, whih employs a rotational spring analogy for the formulation
More informationRelativity fundamentals explained well (I hope) Walter F. Smith, Haverford College
Relativity fundamentals explained well (I hope) Walter F. Smith, Haverford College 3-14-06 1 Propagation of waves through a medium As you ll reall from last semester, when the speed of sound is measured
More informationA NETWORK SIMPLEX ALGORITHM FOR THE MINIMUM COST-BENEFIT NETWORK FLOW PROBLEM
NETWORK SIMPLEX LGORITHM FOR THE MINIMUM COST-BENEFIT NETWORK FLOW PROBLEM Cen Çalışan, Utah Valley University, 800 W. University Parway, Orem, UT 84058, 801-863-6487, en.alisan@uvu.edu BSTRCT The minimum
More informationCase I: 2 users In case of 2 users, the probability of error for user 1 was earlier derived to be 2 A1
MUTLIUSER DETECTION (Letures 9 and 0) 6:33:546 Wireless Communiations Tehnologies Instrutor: Dr. Narayan Mandayam Summary By Shweta Shrivastava (shwetash@winlab.rutgers.edu) bstrat This artile ontinues
More informationDeveloping Excel Macros for Solving Heat Diffusion Problems
Session 50 Developing Exel Maros for Solving Heat Diffusion Problems N. N. Sarker and M. A. Ketkar Department of Engineering Tehnology Prairie View A&M University Prairie View, TX 77446 Abstrat This paper
More informationNumerical Tests of Nucleation Theories for the Ising Models. Abstract
to be submitted to Physial Review E Numerial Tests of Nuleation Theories for the Ising Models Seunghwa Ryu 1 and Wei Cai 2 1 Department of Physis, Stanford University, Stanford, California 94305 2 Department
More informationFrequency Domain Analysis of Concrete Gravity Dam-Reservoir Systems by Wavenumber Approach
Frequeny Domain Analysis of Conrete Gravity Dam-Reservoir Systems by Wavenumber Approah V. Lotfi & A. Samii Department of Civil and Environmental Engineering, Amirkabir University of Tehnology, Tehran,
More informationConveyor trajectory discharge angles
University of Wollongong Researh Online Faulty of Engineering - Papers (Arhive) Faulty of Engineering and Information Sienes 007 Conveyor trajetory disharge angles David B. Hastie University of Wollongong,
More informationThe Reason of Photons Angular Distribution at Electron-Positron Annihilation in a Positron-Emission Tomograph
Advanes in Natural Siene ol 7, No,, pp -5 DOI: 3968/66 ISSN 75-786 [PRINT] ISSN 75-787 [ONLINE] wwwsanadanet wwwsanadaorg The Reason of Photons Angular Distribution at Eletron-Positron Annihilation in
More informationApplying CIECAM02 for Mobile Display Viewing Conditions
Applying CIECAM2 for Mobile Display Viewing Conditions YungKyung Park*, ChangJun Li*, M.. Luo*, Youngshin Kwak**, Du-Sik Park **, and Changyeong Kim**; * University of Leeds, Colour Imaging Lab, UK*, **
More informationAcoustic Waves in a Duct
Aousti Waves in a Dut 1 One-Dimensional Waves The one-dimensional wave approximation is valid when the wavelength λ is muh larger than the diameter of the dut D, λ D. The aousti pressure disturbane p is
More informationRemark 4.1 Unlike Lyapunov theorems, LaSalle s theorem does not require the function V ( x ) to be positive definite.
Leture Remark 4.1 Unlike Lyapunov theorems, LaSalle s theorem does not require the funtion V ( x ) to be positive definite. ost often, our interest will be to show that x( t) as t. For that we will need
More informationBuckling loads of columns of regular polygon cross-section with constant volume and clamped ends
76 Bukling loads of olumns of regular polygon ross-setion with onstant volume and lamped ends Byoung Koo Lee Dept. of Civil Engineering, Wonkwang University, Iksan, Junuk, 7-79, Korea Email: kleest@wonkwang.a.kr
More information12 th Maths Way to Success
th Maths Quarterly Eam-7-Answer Key Part - A Q.No Option Q.No Option Q.No Option Q.No Option 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 Part B. A adj A A adja..() adja A () A I () From (), (),() we get A adja adja
More informationConcerning the Numbers 22p + 1, p Prime
Conerning the Numbers 22p + 1, p Prime By John Brillhart 1. Introdution. In a reent investigation [7] the problem of fatoring numbers of the form 22p + 1, p a, was enountered. Sine 22p + 1 = (2P - 2*
More informationmax min z i i=1 x j k s.t. j=1 x j j:i T j
AM 221: Advaned Optimization Spring 2016 Prof. Yaron Singer Leture 22 April 18th 1 Overview In this leture, we will study the pipage rounding tehnique whih is a deterministi rounding proedure that an be
More informationThe homopolar generator: an analytical example
The homopolar generator: an analytial example Hendrik van Hees August 7, 214 1 Introdution It is surprising that the homopolar generator, invented in one of Faraday s ingenious experiments in 1831, still
More information10.2 The Occurrence of Critical Flow; Controls
10. The Ourrene of Critial Flow; Controls In addition to the type of problem in whih both q and E are initially presribed; there is a problem whih is of pratial interest: Given a value of q, what fators
More informationUPPER-TRUNCATED POWER LAW DISTRIBUTIONS
Fratals, Vol. 9, No. (00) 09 World Sientifi Publishing Company UPPER-TRUNCATED POWER LAW DISTRIBUTIONS STEPHEN M. BURROUGHS and SARAH F. TEBBENS College of Marine Siene, University of South Florida, St.
More information