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CONSTRUCTION OF GENERAL SUBSUMPTIVE SOLUTIONS OF BOOLEAN EQUATIONS VIA COMPLETESUM DERIVATION
"... Booleanequation solving permeates many diverse areas of modern science. To solve a system of Boolean equations, one usually combines them into an equivalent single Boolean equation {f (X) 0}= whose set of solutions is exactly the same as that of the original system of equations. One of the general ..."
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Booleanequation solving permeates many diverse areas of modern science. To solve a system of Boolean equations, one usually combines them into an equivalent single Boolean equation {f (X) 0}= whose set of solutions is exactly the same as that of the original system of equations. One of the general
Efficient Solution of Boolean Equations Using VariableEntered Karnaugh Maps
"... ABSTRACT. A new method for obtaining a compact subsumptive general solution of a system of Boolean equations is presented. The method relies on the use of the variableentered Karnaugh map (VEKM) to achieve successive elimination through successive map folding. It also makes an artificial distinctio ..."
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Cited by 2 (2 self)
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ABSTRACT. A new method for obtaining a compact subsumptive general solution of a system of Boolean equations is presented. The method relies on the use of the variableentered Karnaugh map (VEKM) to achieve successive elimination through successive map folding. It also makes an artificial
Graphbased algorithms for Boolean function manipulation
 IEEE TRANSACTIONS ON COMPUTERS
, 1986
"... In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on th ..."
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Cited by 3499 (47 self)
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In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions
The rendering equation
 Computer Graphics
, 1986
"... ABSTRACT. We present an integral equation which generallzes a variety of known rendering algorithms. In the course of discussing a monte carlo solution we also present a new form of variance reduction, called Hierarchical sampling and give a number of elaborations shows that it may be an efficient n ..."
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Cited by 908 (0 self)
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ABSTRACT. We present an integral equation which generallzes a variety of known rendering algorithms. In the course of discussing a monte carlo solution we also present a new form of variance reduction, called Hierarchical sampling and give a number of elaborations shows that it may be an efficient
USER’S GUIDE TO VISCOSITY SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS
, 1992
"... The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking argume ..."
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Cited by 1403 (15 self)
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The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 560 (10 self)
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We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization
, 2007
"... The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative ..."
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Cited by 568 (23 self)
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for the linear transformation defining the constraints, the minimum rank solution can be recovered by solving a convex optimization problem, namely the minimization of the nuclear norm over the given affine space. We present several random ensembles of equations where the restricted isometry property holds
Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media
 IEEE Trans. Antennas and Propagation
, 1966
"... The characteristics of the waves guided along a plane [I] P. S. Epstein, “On the possibility of electromagnetic surface waves, ” Proc. Nat’l dcad. Sciences, vol. 40, pp. 11581165, Deinterface which separates a semiinfinite region of free cember 1954. space from that of a magnetoionic medium are in ..."
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Cited by 1009 (0 self)
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The characteristics of the waves guided along a plane [I] P. S. Epstein, “On the possibility of electromagnetic surface waves, ” Proc. Nat’l dcad. Sciences, vol. 40, pp. 11581165, Deinterface which separates a semiinfinite region of free cember 1954. space from that of a magnetoionic medium are investi [2] T. Tamir and A. A. Oliner, “The spectrum of electromagnetic waves guided by a plasma layer, ” Proc. IEEE, vol. 51, pp. 317gated for the case in which the static magnetic field is 332, February 1963. oriented perpendicular to the plane interface. It is [3] &I. A. Gintsburg, “Surface waves on the boundary of a plasma in a magnetic field, ” Rasprost. Radwvoln i Ionosf., Trudy found that surface waves exist only when w,<wp and NIZMIRAN L’SSR, no. 17(27), pp. 208215, 1960. that also only for angular frequencies which lie bet\\een [4] S. R. Seshadri and A. Hessel, “Radiation from a source near a plane interface between an isotropic and a gyrotropic dielectric,” we and 1/42 times the upper hybrid resonant frequency. Canad. J. Phys., vol. 42, pp. 21532172, November 1964. The surface waves propagate with a phase velocity [5] G. H. Owpang and S. R. Seshadri, “Guided waves propagating along the magnetostatic field at a plane boundary of a semiwhich is always less than the velocity of electromagnetic infinite magnetoionic medium, ” IEEE Trans. on Miomave waves in free space. The attenuation rates normal to the Tbory and Techniques, vol. MTT14, pp. 136144, March 1966. [6] S. R. Seshadri and T. T. \Vu, “Radiation condition for a maginterface of the surface wave fields in both the media are netoionic medium. ” to be Dublished. examined. Kumerical results of the surface wave characteristics are given for one typical case.
The selfduality equations on a Riemann surface
 Proc. Lond. Math. Soc., III. Ser
, 1987
"... In this paper we shall study a special class of solutions of the selfdual YangMills equations. The original selfduality equations which arose in mathematical physics were defined on Euclidean 4space. The physically relevant solutions were the ones with finite action—the socalled 'instanton ..."
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Cited by 524 (6 self)
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In this paper we shall study a special class of solutions of the selfdual YangMills equations. The original selfduality equations which arose in mathematical physics were defined on Euclidean 4space. The physically relevant solutions were the ones with finite action—the socalled &apos
Gravity with Gravitas: a Solution to the Border Puzzle
, 2001
"... Gravity equations have been widely used to infer trade ow effects of various institutional arrangements. We show that estimated gravity equations do not have a theoretical foundation. This implies both that estimation suffers from omitted variables bias and that comparative statics analysis is unfo ..."
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Cited by 610 (3 self)
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Gravity equations have been widely used to infer trade ow effects of various institutional arrangements. We show that estimated gravity equations do not have a theoretical foundation. This implies both that estimation suffers from omitted variables bias and that comparative statics analysis
Results 1  10
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1,772,411