Search results for "General Mathematics"
showing 10 items of 3795 documents
Indefinite integrals of incomplete elliptic integrals from Jacobi elliptic functions
2017
Integration formulas are derived for the three canonical Legendre elliptic integrals. These formulas are obtained from the differential equations satified by these elliptic integrals when the indep...
Indefinite integrals involving the Jacobi Zeta and Heuman Lambda functions
2017
ABSTRACTJacobian elliptic functions are used to obtain formulas for deriving indefinite integrals for the Jacobi Zeta function and Heuman's Lambda function. Only sample results are presented, mostly obtained from powers of the twelve Glaisher elliptic functions. However, this sample includes all such integrals in the literature, together with many new integrals. The method used is based on the differential equations obeyed by these functions when the independent variable is the argument u of elliptic function theory. The same method was used recently, in a companion paper, to derive similar integrals for the three canonical incomplete elliptic integrals.
Prediction of cardiovascular events with traditional risk equations and total plaque area of carotid atherosclerosis
2021
Abstract A large number of cardiovascular events occur in seemingly healthy individuals. Atherosclerosis imaging can improve the outcome and treatment regime of such subjects. We aim to assess the predictive value of atherosclerosis imaging beyond traditional risk calculators in subjects aged 40–65 years. We compared PROCAM, SCORE and FRAM with carotid ultrasound (total plaque area, TPA) and arterial age (AA) was calculated in subjects without known cardiovascular diseases. Follow-up was obtained by phone or mail. In 2842 subjects (age 50 ± 8, 38% women) 154 (5.4%) cardiovascular events occurred (ASCVD: 41 myocardial infarctions, 16 strokes or TIA, 21 CABG, 41 PTCA, 35 coronary artery disea…
THE CAUCHY DUAL AND 2-ISOMETRIC LIFTINGS OF CONCAVE OPERATORS
2018
We present some 2-isometric lifting and extension results for Hilbert space concave operators. For a special class of concave operators we study their Cauchy dual operators and discuss conditions under which these operators are subnormal. In particular, the quasinormality of compressions of such operators is studied.
INTEGRAL SOLUTIONS TO A CLASS OF NONLOCAL EVOLUTION EQUATIONS
2010
We study the existence of integral solutions to a class of nonlinear evolution equations of the form [Formula: see text] where A : D(A) ⊆ X → 2X is an m-accretive operator on a Banach space X, and f : [0, T] × X → X and [Formula: see text] are given functions. We obtain sufficient conditions for this problem to have a unique integral solution.
Fractional p-Laplacian evolution equations
2016
Abstract In this paper we study the fractional p-Laplacian evolution equation given by u t ( t , x ) = ∫ A 1 | x − y | N + s p | u ( t , y ) − u ( t , x ) | p − 2 ( u ( t , y ) − u ( t , x ) ) d y for x ∈ Ω , t > 0 , 0 s 1 , p ≥ 1 . In a bounded domain Ω we deal with the Dirichlet problem by taking A = R N and u = 0 in R N ∖ Ω , and the Neumann problem by taking A = Ω . We include here the limit case p = 1 that has the extra difficulty of giving a meaning to u ( y ) − u ( x ) | u ( y ) − u ( x ) | when u ( y ) = u ( x ) . We also consider the Cauchy problem in the whole R N by taking A = Ω = R N . We find existence and uniqueness of strong solutions for each of the above mentioned problem…
A logarithmic fourth-order parabolic equation and related logarithmic Sobolev inequalities
2006
A logarithmic fourth-order parabolic equation in one space dimension with periodic boundary conditions is studied. This equation arises in the context of fluctuations of a stationary nonequilibrium interface and in the modeling of quantum semiconductor devices. The existence of global-in-time non-negative weak solutions and some regularity results are shown. Furthermore, we prove that the solution converges exponentially fast to its mean value in the ``entropy norm'' and in the Fisher information, using a new optimal logarithmic Sobolev inequality for higher derivatives. In particular, the rate is independent of the solution and the constant depends only on the initial value of the entropy.
Explicit solutions for a system of coupled Lyapunov differential matrix equations
1987
This paper is concerned with the problem of obtaining explicit expressions of solutions of a system of coupled Lyapunov matrix differential equations of the typewhere Fi, Ai(t), Bi(t), Ci(t) and Dij(t) are m×m complex matrices (members of ℂm×m), for 1≦i, j≦N, and t in the interval [a,b]. When the coefficient matrices of (1.1) are timeinvariant, Dij are scalar multiples of the identity matrix of the type Dij=dijI, where dij are real positive numbers, for 1≦i, j≦N Ci, is the transposed matrix of Bi and Fi = 0, for 1≦i≦N, the Cauchy problem (1.1) arises in control theory of continuous-time jump linear quadratic systems [9–11]. Algorithms for solving the above particular case can be found in [1…
Systèmes hyperboliques d'équations aux dérivées partielles linéaires : régularité et matrices diagonalisables
2001
Resume La regularite des solutions d'un systeme d'equations aux derivees partielles hyperbolique, est liee aux proprietes spectrales d'un faisceaux de matrices reelles. Nous nous interessons ici a la regularite L 2 . Celle ci est obtenue si et seulement si l'exponentielle imaginaire du faisceau est bornee. Nous regardons le lien entre cette condition et les proprietes spectrales du faisceau, ici diagonalisable sur R . Nous donnons en particulier un critere d'exponentielle bornee si les valeurs propres ne sont pas de multiplicites constantes, et nous montrons que dans le cas des faisceaux engendres par deux matrices 3×3, l'exponentielle est bornee si et seulement si le faisceau est analytiqu…
Exact treatment of linear difference equations with noncommutative coefficients
2007
The exact solution of a Cauchy problem related to a linear second-order difference equation with constant noncommutative coefficients is reported.