Class Of Initial Functions Research Articles

Discrete travelling waves in a Toda’s relay chain

A relay version of the Toda’s chain is considered. For a system of m+1 identical oscillators connected in a ring, the applicability of the method of constructing periodic solutions in the form of discrete travelling waves is investigated. These are solutions of the system where all components are represented by the same periodic function with a shift multiple of some parameter Δ. To find the described auxiliary function, the transition to the delayed differential equation is made. The existence of the corresponding periodic solution of the system is ensured by the solvability of the period equation: the value (m+1)Δ must be a multiple of the period of the auxiliary function. This is possible due to the choice of a suitable class of initial functions of the auxiliary equation with delay. The paper describes two families of initial sets for this problem, which correspond to discrete travelling waves of the initial system. It is also proved that the periodic trajectories of the system under consideration lie in the hyperplane orthogonal to the vector consisting of units; results on the instability of the solutions of the system are obtained.

Changing “portrait” of patients with newly diagnosed idiopathic pulmonary hypertension over the past two decades

Objective: to perform a comprehensive analysis of the clinical, functional and hemodynamic status of patients with idiopathic pulmonary hypertension (IPAH) to compare the "portrait" of historical and modern subgroups. Materials and methods. The study included 120 patients with IPAH observed in the Department of Pulmonary Hypertension and Heart Diseases, E.I. Chazov National Medical Research Center of Cardiology. The pts were divided into 2 subgroups depending on the time of diagnosis and were comparable in terms of the initial functional class (WHO). A comparative analysis of clinical, functional, and hemodynamic parameters was carried out. The diagnosis was established according to the algorithm of the Eurasian (2019) and Russian guidelines for the diagnosis and treatment of pulmonary hypertension (PH) (2020). Results. The median time from the onset of PH symptoms to diagnosis in the historical and modern cohorts was 24 months and 13.5 months, respectively, and from the first visit to the diagnosis of IPAH – 13 months and 3.5 months. The median age of patients was 31 years and 40.5 years. In both subgroups, the number of women dominated – up to 86.6 % of patients in the modern cohort. Clinical, laboratory, functional and instrumental tests did not differ significantly between the subgroups. In the structure of concomitant pathology, comorbidity with cardiovascular pathology is most common, in a larger percentage in the modern cohort of patients: hypertension – up to 31.6 %, obesity – up to 25 % and diabetes mellitus – up to 5 %. According to various risk assessment scales, most patients in both subgroups demonstrated intermediate risk at the time of diagnosis, but in the modern cohort, a large proportion of high-risk patients was noted (20.0 %). Conclusion. Nowadays, IPAH remains a late-diagnosed disease, which contributes to a later treatment prescription. The clinical "portrait" of patients with IPAH has changed over the years towards older and more comorbid patients, especially with cardiovascular diseases. Timely detection and treatment of concomitant pathology, timely risk assessment are the key to prescribing the most effective treatment regimens, improving the quality of life and prognosis of patients with IPAH.

Integration of the Kaup–Boussinesq system via inverse scattering method

In this paper, we investigate the Cauchy problem for the KB system in the class of rapidly decreasing functions and give an algorithm of the constructing a solution to the Cauchy problem of the KB system in the class of rapidly decreasing functions via IST method when the scattering coefficient a(k) of the problem (6) has multiple zeros. In this case, the class of initial functions will be expanded by removing the assumption about simplicity of the scattering coefficient a(k) of the problem (6). We also present an efficient method to obtain the time evolution of scattering data. The advantage of this method is its reliability and the possibility of using other soliton equations to obtain the time evolution of scattering data. The resulting equalities completely determine the scattering data at any t, which allows applying the IST method to solve the Cauchy problem for the KB system. The results obtained will be useful in carrying out further analysis in the context of shallow water waves that arises in the context of oceanography.

Possibilities of long-term effective treatment of idiopathic pulmonary arterial hypertension by replacing sildenafil with riociguat and using sequential combination therapy: case report

Modern pathogenetic therapy of idiopathic pulmonary arterial hypertension (IPAH), a severe life-threatening cardiovascular disease of unknown etiology, leads to a positive clinical effect due to reverse remodeling of the vessels of the microvasculature of the lungs. Highly effective drugs of specific therapy that act on the main targets of pathogenesis have now been introduced into clinical practice.The presented clinical case of a patient with diagnosed in 2014 IPAH with an initial functional class III according to the WHO classification demonstrates high long-term efficacy and safety of specific therapy based on the use of the soluble guanylate cyclase stimulator riociguat for 5 years after replacing previous therapy with sildenafil with further implementation of the strategy of sequential combination therapy due to the addition of ambrisentan and selexipag.

Characterization of heart failure patients with reverse left ventricular remodelling post-angiotensin receptor blockers/neprilysin inhibitors therapy.

AimsTo assess the effect of angiotensin receptor blockers/neprilysin inhibitors (ARNI) on left ventricular (LV) ejection fraction (LVEF) and LV dimensions in a real‐life cohort of heart failure and reduced ejection fraction (HFrEF) patients, while analysing patient characteristics that may predict reverse LV remodelling.Methods and resultsThe ARNI‐treated HFrEF patients followed at a single tertiary medical centre HF‐outpatient clinic were included in the study. Clinical and echocardiographic parameters were evaluated prior to ARNI initiation, and while on ARNI therapy, assessing patient characteristics associated with reverse LV remodelling. The cohort included 91 patients (mean age 60.5 years, 90% male) and 47 (52%) patients exhibited ARNI responsiveness, defined as an increase in LVEF during therapy. Overall, LVEF increased by 19% post‐ARNI (23.8 to 28.4%, P < 0.001). Subgroup analysis revealed several parameters associated with significant LVEF improvement, including baseline LVEF <30%, non‐ischaemic HF aetiology, lack of cardiac resynchronization therapy (CRT), better initial functional class and ARNI initiation within 3 years from HF diagnosis (P ≤ 0.001 for all). Significant reduction in LV dimensions was noted in patients with lower initial LVEF, non‐ischaemic HF and no CRT. Further combined subgrouping of the study population demonstrated that patients with both LVEF <30% and a non‐ischaemic HF gained most benefit from ARNI with an average of 51% improvement in LVEF (19.9 to 30%, P < 0.001).ConclusionsThe ARNI treatment response is not uniform among HFrEF patient subgroups. More pronounce reverse LV remodelling is associated with early ARNI treatment initiation in the course of HFrEF, and in those with LVEF <30%, non‐ischaemic HF and no CRT.

Fourier transform method for partial differential equations: Formulas for representing solutions to the Cauchy problem

The paper proposes a method for solving the Cauchy problem for linear partial differential equations with variable coefficients of a special form, allowing, after applying the (inverse) Fourier transform, to rewrite the original problem as a Cauchy problem for first-order partial differential equations. The resulting problem is solved by the method of characteristics and the (direct) Fourier transform is applied to its solution. And for this it is necessary to know the solution of the Cauchy problem for a first-order equation in the entire domain of definition. This leads to the requirement that the support of the (inverse) Fourier transform of the initial function of the original problem be compact, and to describe the class of initial functions, it is necessary to use Paley -Wiener - Schwarz-type theorems on Fourierimages, including distributions. The presentation of solutions in the form of the Fourier transform of some function (distribution), determined by the initial function, is presented. A general form of the evolutionary equation is written down, which, when the described method is applied, leads to the consideration of a homogeneous first-order equation, and a formula for the solution of the Cauchy problem in this general case is derived. The general form of the equation is written down, which leads to the consideration of a first-order inhomogeneous equation, and a formula for solutions it is derived. Particular cases of these equations are the well-known equations that are encountered in the description of various processes in physics, chemistry, and biology.

Constructions of balanced Boolean functions on even number of variables with maximum absolute value in autocorrelation spectra [formula omitted

The autocorrelation properties of Boolean functions are closely related to the Shannon’s concept of diffusion and can be accompanied with other cryptographic criteria (such as high nonlinearity and algebraic degree) for ensuring an overall robustness to various cryptanalytic methods. In a series of recent articles [14,9,15], the design methods of n-variable balanced Boolean functions n is strictly even) with small absolute indicator Δf < 2n/2 have been considered. Whereas the two first articles managed to solve this problem for relatively large n⩾46, a recent approach [15] has introduced a generic design framework achieving Δf < 2n/2 for even n⩾22. Based on a suitable modification of the method of Rothaus, used to construct new bent functions from known ones, we provide a generic iterative framework for designing balanced functions satisfying the condition Δf < 2n/2 and having overall good cryptographic properties for any even n⩾12. Even though the problem of specifying functions having Δf < 2n/2 for smaller n has been considered in [14,9,15] using various search algorithms, our method for the first time provides relatively simple iterative framework for variable spaces of more practical interest. Moreover, our approach can be efficiently applied to certain classes of initial functions (derived from partial spread bent functions) for deriving balanced functions with Δf < 2n/2 for relatively large n, namely for n⩾48 satisfying n≡0 mod 4 and n⩾54 with n≡2 mod 4. In the latter case, our nonlinearity bound is better than the one presented in [14].

Convergence to traveling waves for time-periodic bistable reaction-diffusion equations

We consider the equation u t = u x x + f ( t , u ) u_t=u_{xx} +f(t,u) , x ∈ R x\in \mathbb {R} , t &gt; 0 t&gt;0 , where f ( t , x ) f(t,x) periodically depends on t t and is of bistable type. Classical results showed that for a large class of initial functions, the solutions converge to a periodic traveling wave if it connects two linearly stable time-periodic states. Under some conditions on the initial functions, we prove this convergence result by a new approach which allows the time-periodic states to be degenerate.

On the critical exponent “instantaneous blow-up” versus “local solubility” in the Cauchy problem for a model equation of Sobolev type

We consider the Cauchy problem for a model partial differential equation of order three with a non-linearity of the form . We prove that when the Cauchy problem in has no local-in-time weak solution for a large class of initial functions, while when there is a local weak solution.

On Large-Time Behavior of Solutions of Parabolic Equations

We study the stabilization of solutions of the Cauchy problem for second-order parabolic equations depending on the behavior of the lower-order coefficients of equations at the infinity and on the growth rate of initial functions. We also consider the stabilization of solution of the first boundary-value problem for a parabolic equation without lower-order coefficients depending on the domain Q where the initial function is defined for t =0.&#x0D; In the first chapter, we study sufficient conditions for uniform in x on a compact K RN stabilization to zero of the solution of the Cauchy problem with divergent elliptic operator and coefficients independent of t and depending only on x. We consider classes of initial functions:&#x0D; &#x0D; bounded in RN,&#x0D; with power growth rate at the infinity in RN,&#x0D; with exponential order at the infinity.&#x0D; &#x0D; Using examples, we show that sufficient conditions are sharp and, moreover, do not allow the uniform in RN stabilization to zero of the solution of the Cauchy problem.&#x0D; In the second chapter, we study the Cauchy problem with elliptic nondivergent operator and coefficients depending on x and t. In different classes of growing initial functions we obtain exact sufficient conditions for stabilization of solutions of the corresponding Cauchy problem uniformly in x on any compact K in RN. We consider examples proving the sharpness of these conditions.&#x0D; In the third chapter, for the solution of the first boundary-value problem without lower-order terms, we obtain necessary and sufficient conditions of uniform in x on any compact in Q stabilization to zero in terms of the domain RN \ Q where Q is the definitional domain of the initial function for t =0. We establish the power estimate for the rate of stabilization of the solution of the boundary-value problem with bounded initial function in the case where RN \ Q is a cone for t =0.

On critical exponents for weak solutions of the Cauchy problem for a non-linear equation of composite type

We consider the Cauchy problem for a model partial differential equation of third order with non-linearity of the form , where for and . We construct a fundamental solution for the linear part of the equation and use it to obtain analogues of Green’s third formula for elliptic operators, first in a bounded domain and then in unbounded domains. We derive an integral equation for classical solutions of the Cauchy problem. A separate study of this equation yields that it has a unique inextensible-in-time solution in weighted spaces of bounded and continuous functions. We prove that every solution of the integral equation is a local-in-time weak solution of the Cauchy problem provided that . When , we use Pokhozhaev’s non-linear capacity method to show that the Cauchy problem has no local-in-time weak solutions for a large class of initial functions. When , this method enables us to prove that the Cauchy problem has no global-in-time weak solutions for a large class of initial functions.

Instantaneous blow-up versus local solubility of the Cauchy problem for a two-dimensional equation of a semiconductor with heating

We consider the Cauchy problem for a model third-order partial differential equation with non-linearity of the form . We prove that for the Cauchy problem in has no local-in-time weak solution for a large class of initial functions, while for a local weak solution exists.

Local existence and nonexistence for reaction-diffusion systems with coupled exponential nonlinearities

We study the reaction-diffusion system with coupled exponential nonlinearities{∂tu=Δu+ep1u+p2vin Ω×(0,T),∂tv=Δv+eq1u+q2vin Ω×(0,T),u(x,t)=v(x,t)=0on ∂Ω×(0,T),u(x,0)=u0(x),v(x,0)=v0(x)in Ω, where T>0, pi≥0 and qi≥0(i=1,2) with (p1,p2)≠(0,0) and (q1,q2)≠(0,0). The domain Ω is RN(N≥1) or a bounded domain in RN with C2 boundary and the initial functions u0 and v0 are nonnegative and measurable. For each (p1,p2,q1,q2), we obtain integrability conditions of (u0,v0) which explicitly determine the existence/nonexistence of a local in time nonnegative classical solution. For the existence result, we can take a wider class of initial functions than previously suggested. Our analysis can be applied to other nonlinearities including superexponential ones.

PIH13 - Annual Direct Medical Cost of Pediatric Pulmonary Hypertension Health Care in Centro Medico Nacional 20 De Noviembre (Nmcissste, Mexico)

To estimate the burden of annual costs for Pediatric Pulmonary Hypertension (PPH) health care considering the public perspective in Mexico. A retrospective cohort study was conducted using medical records from a pediatric cardiology service at NMC ISSSTE, Mexico City. All patients who had PPH included were aged under 18 years (2013-2015). Clinical and economic variables were collected; direct healthcare costs were medical visits, hospitalization days, emergency visits, diagnostic or therapeutic procedures and medication. Prescriptions (acute, chronic, or upon request) were quantified based on mean dosage/patient, all resources used was obtained directly from patient´s charts and prices were obtained from www. compranet.funcionpublica.gob.mx. A descriptive analysis was performed, the bivariate analysis included linear correlation and mean differences, costs were compared by ANOVA test of initial functional class. A log linear regression model was done, p value <0.05 was consider statistically significant. The cost was expressed in USD (1USD =$18.8113 Mx, www. banxico.org Jan 2018). A total of 84 patients, were identified, 46% males, the mean of age at diagnosis 8.6±4.5 years (yrs.), median follow-up 4 yrs., the functional class (FC) distribution was as following: FC I: 33, FCII 26, FCIII:7, FC IV 2, and 2 unknown. The cost average per patient/year estimated was $81, 820 CI 95% ($79,022 - $84619), and institutional annual total cost $1,299,937.75 CI 95% ($1,156,407, $1,443,468), the average of cost by FC I: $52,223.46, FCII, $63,301.89 FCIII: $89,151.56, FC IV $121,463.65. According with log linear regression model the cost per patient at first year was $101,535.14, the total costs were associated to age, FC, number of hospitalization, and medication p value 0.0394, .049 y p<0.000 respectively. PPH had a substantial economic burden during first year on the health care system (0.032%), the FC, hospitalization and medication were associated with annual total cost.

Factors influencing outcomes in patients with Eisenmenger syndrome: a nine-year follow-up study.

In patients with Eisenmenger syndrome, life expectancy is usually longer than in patients with other forms of pulmonary arterial hypertension (PAH). We conducted a cohort study in which patients were followed over a long period of time in an attempt to identify potential predictors of clinical outcomes. Sixty-seven treatment-naïve patients were enrolled (age range = 12–60 years; median age = 33 years). Baseline demographic, diagnostic, and functional parameters, plasma levels of endothelial dysfunction markers, and treatment-related data were tested for possible correlations with event-free survival. Patients were started on oral PAH drugs at the beginning of follow-up (n = 23), during follow-up (n = 33), or remained untreated (n = 11). The duration of follow-up was 0.54–9.89 years (median = 7.13 years), with an overall survival rate of 82% and an event-free survival rate of 70%. The estimated mean for event-free survival time was 7.71 years (95% confidence interval [CI] = 6.86–8.55 years). Of the 16 variables that were analyzed, the duration of exposure to PAH drugs was identified as an independent protective factor (hazard ratio [HR] = 0.25 for quartiles, 95% CI = 0.14–0.47, P < 0.001). The initial functional class (HR = 3.07; 95% CI = 1.01–9.34; P = 0.048), the severity of right ventricular dysfunction (HR = 2.51 [mild, moderate or severe dysfunction]; 95% CI = 1.22–5.19; P = 0.013) and plasma von Willebrand factor concentration (HR = 1.74 for quartiles; 95% CI = 1.07–2.83; P = 0.026) were identified as risk factors. The length of exposure to oral PAH therapies influences survival favorably in Eisenmenger patients. This may be of interest for communities where access to medications is restricted.

Travelling wave solutions of a parabolic-hyperbolic system for contact inhibition of cell-growth

We consider a cell growth model involving a nonlinear system of partial differential equations which describes the growth of two types of cell populations with contact inhibition. Numerical experiments show that there is a parameter regime where, for a large class of initial data, the large time behaviour of the solutions is described by a segregated travelling wave solution with positive wave speed c. Here, the word segregated expresses the fact that the different types of cells are spatially segregated, and that the single densities are discontinuous at the moving interface which separates the two populations. In this paper, we show that, for each wave speed c &gt; c, there exists an overlapping travelling wave solution, whose profile is continuous and no longer segregated. We also show that, for a large class of initial functions, the overlapping travelling wave solutions cannot represent the large time profile of the solutions of the system of partial differential equations. The structure of the travelling wave solutions strongly resembles that of the scalar Fisher-KPP equation, for which the special role played by the travelling wave solution with minimal speed has been extensively studied.

SUCCESSFUL TREATMENT OF INOPERABLE THROMBOEMBOLIC PULMONARY HYPERTENSION PATIENT WITH SILDENAFIL IN HIGH DOSES

The currentguidelines on chronic thromboembolic pulmonary hypertension (CTEPH) treatment consider pulmonary thrombendarterectomy as the first therapy choice. In case of inoperability due to severe patient's condition, distal lesions of pulmonary vessels, extremely high pulmonary vascular resistance, medical treatment for CTEPH includes life-long anticoagulation therapy and reduction of heart failure symptoms. This clinical case of the 59-y-old patient M. with inoperable CTEPH demonstrates the efficacy of phosphodiеsterase-5 inhibitor Sildenafil usedin high doses. The diagnosis was confirmed by the results of the complete diagnostic process including right heart catheterization and pulmonary angiography. The initial functional class was assessed as III in accordance with WHO classification. Sildenafil 60 mg daily was added tothe standard therapy (anticoagulant, calcium channel blocker) for initial four weeks. To the 4wk visit Sildenafil dose was increased to 240 mgdailytaking into account good tolerance of the treatment.The significant improvement of functional class, positive dynamic ofhemodynamic and echo parameters were found to 4 month of follow-up.

A Lotka–Volterra cooperating reaction–diffusion system with degenerate density-dependent diffusion

In the Lotka–Volterra cooperating reaction–diffusion system if the diffusion coefficients are constants then for a certain set of reaction rates in the reaction function the solution of the system blows up in finite time, and for another set of reaction rates, a unique global solution exists and converges to the trivial solution. However, if the diffusion coefficients are density-dependent then the dynamic behavior of the solution can be quite different. The aim of this paper is to investigate the global existence and the asymptotic behavior of the solution for a class of density-dependent cooperating reaction–diffusion systems where the diffusion coefficients are degenerate. It is shown that the time-dependent problem has a unique bounded global solution, and in addition to the trivial and semi-trivial solutions the corresponding steady-state problem has a positive maximal solution and a positive minimal solution. Moreover, the time-dependent solution converges to the maximal solution for one class of initial functions, and to the minimal solution for another class of initial functions. The above convergence property holds true for any reaction rates in the reaction function. Applications of the above results are given to a porous medium type of reaction–diffusion problem as well as other types of diffusion coefficients, including the finite sum and products of these functions.

Echocardiographic Predictors of Reverse Remodeling After Cardiac Resynchronization Therapy and Subsequent Events

Studies of echocardiographic predictors of response after cardiac resynchronization therapy (CRT) have largely involved single parameters. We hypothesized that combining parameters would be more robust and sought to develop a multiparametric echocardiographic score for predicting CRT response. Global longitudinal strain of left ventricle was added to standard echocardiographic measurements in 334 consecutive patients (224 men; mean, 65±12 years) who underwent baseline echocardiography before CRT and underwent follow-up echocardiograms at 1 year. Regression analysis was performed to create an echocardiographic score for prediction of LV reverse remodeling (defined as ≥15% reduction in the LV end-systolic volume). Cox proportional hazards models were used to identify the association of the score with death, transplantation or LV assist device implantation, and heart failure hospitalization during 57±22 months of follow-up. LV reverse remodeling (n=161; 48%) was associated with pre-CRT LV end-diastolic dimension index <3.1 cm/m(2), global longitudinal strain of left ventricle <-7%, left atrial area <26 cm(2), right ventricular end-diastolic area index <10.0 cm(2)/m(2), right atrial area <20 cm(2), and right ventricular fractional area change ≥35%. Combination of these into an echocardiographic score allowed prediction of LV reverse remodeling with a sensitivity of 84% and a specificity of 79%. During follow-up, there were 134 deaths, 18 heart transplantations/LV assist device implantations, and 93 heart failure admissions. The score was associated with heart failure admission, heart transplantation/LV assist device, or death (hazard ratio, 0.97; 95% confidence interval, 0.95-0.98; P<0.001) and all-cause death (hazard ratio, 0.97; 95% confidence interval, 0.96-0.98; P<0.001), independent of age, sex, ischemic cause, and initial functional class. A multiparametric echocardiographic score is helpful in selecting patients likely to undergo reverse remodeling after CRT and predicts clinical outcomes.

Positive solutions of quasilinear parabolic systems with Dirichlet boundary condition

Coupled systems for a class of quasilinear parabolic equations and the corresponding elliptic systems, including systems of parabolic and ordinary differential equations are investigated. The aim of this paper is to show the existence, uniqueness, and asymptotic behavior of time-dependent solutions. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients D i ( u i ) may have the property D i ( 0 ) = 0 for some or all i = 1 , … , N , and the boundary condition is u i = 0 . Using the method of upper and lower solutions, we show that a unique global classical time-dependent solution exists and converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a scalar polynomial growth problem, a coupled system of polynomial growth problem, and a two component competition model in ecology.