Differential Equations最新文献

Purpose: This study examined the effectiveness and safety of a home-based pulmonary rehabilitation (HBPR) program in Veterans. Methods: Patients were evaluated from five Veteran Affairs facilities that enrolled in the 12-week program. Pre- to postchanges were completed on clinical outcomes using paired t-tests and the Wilcoxon signed rank sum test. Descriptive statistics were used for patient demographics, emergency room visits, and hospitalizations. Results: Two hundred eighty-five patients with a mean age of 69.6 ± 8.3 years enrolled in the HBPR program from October 2018 to March 2020. There was a 62% (n = 176) completion rate of both pre- and post assessments. Significant improvements were detected after completion of the HBPR program in dyspnea (modified Medical Research Council: 3.1 ± 1.1 vs. 1.9 ± 1.1; p < 0.0001); exercise capacity (six-minute walk distance: 263.1 m ± 96.6 m vs. 311.0 m ± 103.6 m; p < 0.0001; Duke Activity Status Index: 13.8 ± 9.6 vs. 20.0 ± 12.7; p < 0.0001; self-reported steps per day: 1514.5 ± 1360.4 vs. 3033.8 ± 2716.2; p < 0.0001); depression (patient health questionnaire-9: 8.3 ± 5.7 vs. 6.4 ± 5.1); nutrition habits (rate your plate, heart: 45.3 ± 9.0 vs. 48.9 ± 9.2; p < 0.0001); multicomponent assessment tools (BODE Index: 5.1 ± 2.5 vs. 3.4 ± 2.4; p < 0.0001), GOLD ABCD Assessment: p < 0.0009); and quality of life (chronic obstructive pulmonary disease assessment test: 25.4 ± 7.7 vs. 18.7 ± 8.5; p < 0.0001). No adverse events were reported due to participation in HBPR. Conclusions: The HBPR program is a safe and effective model and provides an additional option to address the gap in pulmonary rehabilitation access and utilization in the Veterans Affairs.

Abstract

In this paper, we obtain two-sided a priori estimates for the solution of a homogeneousthird-order Volterra integro-differential equation with a power-law nonlinearity and differencekernel. It is shown that the lower a priori estimate, which plays the role of a weight function whenconstructing a metric in the cone of the space of continuous functions, is sharp. Using theseestimates, by the weighted metric method (an analog of A. Bielecki’s method), we prove a globaltheorem on the existence and uniqueness of a nontrivial solution of the initial value problem forthis integro-differential equation in the class of nonnegative continuous functions on the positivehalf-line and on the method for finding this solution. It is shown that the solution can be found bythe successive approximation method, and an estimate of the rate of convergence of theapproximations to the exact solution is obtained. Examples are given to illustrate the resultsobtained.

Abstract

We discuss the well-posed solvability and exponential stability of solutions of abstractintegro-differential equations where the kernels of integral operators are of general type and lie inthe space of functions integrable on the positive half-line. The abstract integro-differentialequations studied in the present paper are operator models of viscoelasticity theory problems. Theproposed approach to the study of these integro-differential equations is related to an applicationof semigroup theory and can also be used to study other integro-differential equations containingintegral terms of the Volterra convolution type.

Abstract

For any finite set of nonnegative numbers containing zero, we construct a two-dimensionallinear homogeneous differential system (periodic if all elements of the given set are pairwisecommensurate) in which the spectra of the oscillation exponents of signs, zeros, roots, andhyperroots coincide with this set, and all the values of these exponents are essential.

Abstract

We consider a singularly perturbed optimal tracking problem with a given reference pathin the case of incomplete information about the state vector in the presence of exogenousdisturbances. To analyze the differential equations that arise when solving this problem, we usethe decomposition method, which is based on the technique of integral manifolds of fast and slowmotions.

Abstract

Using recurrence relations between any three consecutive polynomial eigenfunctions ofsecond-order linear differential equations, the Christoffel–Darboux formulas are derived for thesystem of polynomial eigenfunctions of these equations.

Abstract

An approach is proposed to constructing a digital controller that stabilizes acontinuous-time switched linear system with commensurate delays in control under slowswitchings. The approach to stabilization consistently includes the construction of a switchedcontinuous–discrete-time closed-loop system with a digital controller, the transition to itsdiscrete-time model, represented in the form of a switched system with modes of different orders,simultaneous stabilization of the subsystems of the resulting discrete-time model, and calculationof a delay time that ensures the stability of the original switched system closed by the controllerfound.

Abstract

This paper proposes a new approach to the study of direct and inverse problems for asingularly perturbed heat equation with nonlinear temperature-dependent diffusion, based on thefurther development and use of asymptotic analysis methods in the nonlinear singularly perturbedreaction–diffusion–advection problems. The essence of the approach is presented using theexample of one class of one-dimensional stationary problems with nonlinear boundary conditions,for which the case of applicability of asymptotic analysis is singled out. Sufficient conditions forthe existence of classical solutions of the boundary layer type and the type of contrast structuresare formulated, asymptotic approximations of an arbitrary order of accuracy to such solutions areconstructed, algorithms for constructing formal asymptotics are substantiated, and the Lyapunovasymptotic stability of stationary solutions with boundary and internal layers as solutions of thecorresponding parabolic problems is investigated. A class of nonlinear problems that take intoaccount lateral heat exchange with the environment according to Newton’s law is considered.A theorem on the existence and uniqueness of a classical solution with boundary layers inproblems of this type is proved. As applications of this research, methods for solving specificdirect and inverse problems of nonlinear heat transfer related to increasing the operating efficiencyof rectilinear heating elements in the smelting furnaces (heat exchangers) are presented, whichinclude the calculation of thermal fields in the heating elements and a method for reconstructingthermal diffusion and heat transfer coefficients based on modeling data.

Abstract

An inverse problem for a second-order hyperbolic equation containing two nonlinear termsis studied. The problem is to reconstruct the coefficients of the nonlinearities. The Cauchyproblem with a point source located at a point (mathbf {y}) isconsidered. This point is a parameter of the problem and successively runs over a spherical surface(S ). It is assumed that the desired coefficients arenonzero only in a domain lying inside (S). The trace of thesolution of the Cauchy problem on (S) is specified for allpossible values of ( mathbf {y}) and for times close to the arrival ofthe wave from the source to the points on the surface (S ); this allows reducing the inverse problem underconsideration to two successively solved problems of integral geometry. Solution stability estimatesare found for these two problems.