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In the paper, ideas of the Lomov regularization method are generalized to the Cauchy problem for a singularly perturbed partial integro-differential equation in the case when the integral term contains a rapidly varying kernel. Regularization of the problem is carried out, the normal and unique solvability of general iterative problems is proved.

OBJECTIVES/HYPOTHESIS Upper respiratory tract infections are a common cause of temporary and permanent olfactory dysfunction in the general population. Postviral or postinfectious olfactory loss (PIOL) develops only in rare cases. The aim of this study was to investigate the anatomical features of olfactory cleft (OC) in patients with PIOL to shed light on possible predisposing factors for PIOL. STUDY DESIGN Retrospective study. METHODS We retrospectively evaluated paranasal sinus computed tomography (CT) scan results of patients diagnosed with PIOL. A control group consisted of normosmic individuals who underwent paranasal sinus CT scans before septoplasty surgery. We compared the olfactory fossa depth, OC width, and volume on the CT scans of the PIOL and control groups. RESULTS In total, 71 individuals fulfilled the study criteria (PIOL group, n = 32; control group, n = 39). There was no statistically significant difference in the olfactory fossa depth in the two groups. The OC width and volume in the PIOL group was found to be significantly increased than that in the control group (P

This paper presents a numerical realization of the Navier-Stokes equations in irregular domains using the fictitious domain method with a continuation along with the lowest coefficient. To solve numerous connected issues in irregular regions, the fictitious domain method is broadly used. The advantage of the fictitious domain method is that the problem is solved not in the original complex domain, but in a few other, easier domains. Using the method, computation is done easily for a sufficiently wide class of problems with arbitrary computational domains. The problem is solved using two methods. The primary method is based on the development of a distinct issue in variables of the stream function and the vortex velocity using the pressure uniqueness condition. The second method is to understand the expressed issue by the fictitious domain method with a continuation by lower coefficients. Using the fictitious domain method, a computational algorithm is constructed based on the explicit finite difference schemes. The finite difference scheme is stable and has high computational accuracy and it gives the possibility to parallelize. Temperature distributions and stream functions are presented as numerical results. A parallel algorithm has been developed using Open Multi-Processing (hereinafter OpenMP) and Message Passing Interface (hereinafter MPI) technologies. Within the parallel approach, we used OpenMP technology for parallel calculation of vorticity and stream work, and for calculating temperature we applied MPI technology. The performance analysis on our parallel code shows favorable strong and weak scalability. The test results show that the code running in the parallel approach gives the expected results by comparing our results with those obtained while running the same simulation on the central processing unit (CPU), У даній роботі представлена чисельна реалізація рівнянь Нав’є-Стокса в нерегулярних областях з використанням методу фіктивних областей з продовженням за найменшим коефіцієнтом. Метод фіктивних областей широко використовується для вирішення численних пов’язаних задач у нерегулярних областях. Перевага методу фіктивних областей полягає у тому, що задача вирішується не в вихідній складній області, а в декількох інших, простіших областях. За допомогою даного методу легко виконуються обчислення для досить широкого класу задач з довільними розрахунковими областями. Задача вирішується двома способами. Основний метод заснований на розробці окремої задачі в змінних функції потоку та швидкості вихору з використанням умови унікальності тиску. Другий метод полягає у розумінні вираженої проблеми методом фіктивних областей з продовженням за нижчими коефіцієнтами. За допомогою методу фіктивних областей побудований обчислювальний алгоритм на основі явних кінцево-різницевих схем. Кінцево-різницева схема стійка, має високу обчислювальну точність і дає можливість розпаралелювання. Розподіл температури та функції потоку представлені у вигляді чисельних результатів. Розроблено паралельний алгоритм з використанням технологій відкритої багатопроцесорної обробки (далі OpenMP) та інтерфейсу передачі повідомлень (далі MPI). В рамках паралельного підходу ми використовували технологію OpenMP для паралельного розрахунку завихореності та роботи потоку, а для розрахунку температури ми застосували технологію MPI. Аналіз продуктивності нашого паралельного коду показує сприятливу сильну та слабку масштабованість. Результати випробувань показують, що код, який виконується при паралельному підході, дає очікувані результати, порівнюючи наші результати з результатами, отриманими під час виконання того ж моделювання на центральному процесорі (ЦП)

Objective: The development of otologic surgical techniques has significantly improved the functional results of surgery. However, the issue of the most effective ossiculoplasty material is still controversial. The study aimed to introduce a novel method of autologous ossiculoplasty, using “ionomer bone cement coated mastoid cortical bone” and to assess short-term and long-term results of this method. Material and Methods: The study presented a retrospective, consecutive case series of twelve patients who underwent revision surgery as type IV tympanoplasty using Mastoid cortical bone coated with ionomer bone cement in our institution between January 2013 and December 2019. Coating with ionomer bone cement was performed to prevent the autograft from sticking to the surrounding bone tissue. The short- and long-term auditory functions and otologic examination findings of the patients were analyzed. Results: Physical examination findings were satisfactory. Except one, all patients had a significant improvement in hearing outcomes, and the late-term results were also satisfactory. An average long term audiological gain of 19.9 dB (± 8.7 SD) was found. Conclusion: A novel method of Hybrid Ossiculoplasty: Ionomer Bone Cement Coated Mastoid Cortical Bone is an effective and safe method of ossiculoplasty. It can be easily eliminated one of the major disadvantages of mastoid cortical bone by coating it with ionomer bone cement.

In this paper, we study numerical methods for solving the Navier-Stokes equations in doubly connected domains. Two methods for solving the problem are considered. The first method is based on constructing a difference problem in variables of the stream function and the vortex of velocity using the uniqueness condition for pressure. The numerical solution of the elliptic equation for stream functions is found as the sum of the solutions of two simple problems of an elliptic type. One problem is with homogeneous boundary conditions, and the other is with a homogeneous equation. An alternative approach to solving the problem is the fictitious domain method with the continuation of the least coefficient. This method does not require satisfying the pressure uniqueness condition, and is simple to implement. An important direction in the development of numerical simulation methods is the study of approximate methods for solving problems of mathematical physics in complex multidimensional areas. To solve many applied problems in irregular areas, the fictitious domain method is widely used, which is characterized by a high degree of automation of programming. The main idea of the fictitious domain method is that the problem is solved not in the original complex domain, but in some other, simpler domain. This allows to create software immediately for a fairly wide class of problems with arbitrary computational domains. The possibilities of applying the fictitious domain method to the problems of hydrodynamics in the variables “stream function, vortex of velocity” are considered in many works. In this paper, we study a numerical method for solving the Navier-Stokes equations in doubly connected domains. A computational finite difference algorithm for solving an auxiliary problem of the fictitious domain method has been developed. The results of numerical modeling of the two-dimensional Navier-Stokes equations by the fictitious domain method with continuation by the lowest coefficient are presented. For this problem, a parallel algorithm was developed using the CUDA architecture, which was tested on various grid dimensions.

An important direction in the development of numerical simulation methods is the study of approximate methods for solving problems of mathematical physics in complex multidimensional fields. To solve many applied problems in irregular areas, the method of fictitious areas is widely used, which is characterized by a high degree of automation of programming. The main idea of the method of fictitious domains is that the problem is solved not in the original complex domain, but in some other, simpler domain. This allows you to create software immediately for a fairly wide class of problems with arbitrary computational domains. The possibilities of applying the method of fictitious domains to the problems of hydrodynamics in the variables “stream function, velocity vortex” have been considered in many works. In this paper, we study a numerical method for solving the Navier-Stokes equations in doubly connected domains. To solve the two-dimensional Navier-Stokes equations in irregular domains, an approximate method based on the method of fictitious domains is proposed. A computational finite difference algorithm for solving an auxiliary problem of the method of fictitious domains has been developed. The results of numerical simulation of two-dimensional Navier-Stokes equations by the method of fictitious domains with continuation by the lowest coefficient are presented. For this problem, a parallel algorithm was developed using CUDA technologies, which was tested on various mesh dimensions

In this paper, the theory of conjugate equations is used to solve the inverse problem of the continuation of potential fields in the direction of disturbing masses, in the inverse problem of magnetotelluric sounding (MTS), for problems of mathematical epidemiology.

In this paper, we consider a variant of the fictitious domain method associated with the modification of nonlinear terms in a fictitious subdomain. The model problem shows the effectiveness of using this modification. The proposed version of the method is used to solve the problem of an arbitrary region and to set a boundary condition for pressure. A numerical solution is implemented and the results of numerical results are given.

Purpose: To investigate potential pathological differences in major brain metabolites in burning mouth syndrome (BMS). Materials and Methods: We prospectively evaluated eight patients and six healthy controls with single voxel magnetic resonance (MR) spectroscopy throughout 2017 using 3-Tesla MR unit. Metabolite levels measured from the left posterior paracingulate white matter. Raw images were processed with Tarquin version 4.3.10 and area under curve values were automatically calculated for GABA (γ-Aminobutyric acid), Ins (myo-inositole), tNAA (N-Acetylaspartate), tCho (total choline), tCr (total creatine) and GLx (glutamine + Glutamat). Major metabolite levels and all metabolites ratio to tCr calculated and compared between two groups using Mann-Whitney U test. Results: GABA/tCR value of the patients (0.589 ± 0.194, median = 0.515) was significantly higher than control group (0.230 ± 0.067, median = 0.220) (P = 0.002). tNAA/tCR value of the patients (1.106 ± 0.218, median: 1.205), was significantly lower than the control group (1.538 ± 0.401, median: 1.705) (P = 0.028). No significant difference was observed between two groups in terms of all other metabolites (P > 0.05). Conclusion: We demonstrated increased GABA and decreased NAA in the left posterior paracingulate region in BMS patients. We suggest that these metabolite alterations in central nervous system might play a key role in the etiology of the disease by inhibiting the suppression of burning sensation.

Several numerical methods can be used to approximate the solution of the problem. In order to determine the most effective of them, it is necessary to carefully study each method. The most efficient approximation method is characterized by properties such as high accuracy of the solution, fewer iterations and parameters in the calculation, calculation speed, etc. In this paper we consider the Dirichlet problem for the Poisson equation described by the initial-boundary value problem for the elliptic type of the second order. As an effective iterative method for its approximate solution, variational methods for constructing difference equations and variational methods for constructing iterative algorithms were used. The article presents the results of calculations developed using the variational method for the selected model problem. Examples of calculations for model problems are given. The results of the computational experiment demonstrate the high efficiency of the proposed iterative method.

The neutrophil-to-lymphocyte ratio (NLR), platelet-to-lymphocyte ratio (PLR), and mean platelet volume (MPV) are markers of subclinical inflammation and atherothrombosis. We investigated whether these easily accessible blood count parameters are affected by peripheral vertigo (PV). We studied 142 patients who were diagnosed with PV and referred to our hospital along with 135 healthy patients who were free of inflammation as a control group. The patient group was divided into 3 study groups depending on the presence of benign paroxysmal positional vertigo (BPPV): BPPV, vestibular dysfunction (VD), and BPPV + VD. The total patient group and 3 subgroups were compared to the control group with respect to the NLR, PLR, and MPV. The NLR and PLR were calculated by dividing the neutrophil and platelet values by the lymphocyte value. Of 142 patients, 43, 71, and 28 patients comprised the BPPV, VD, and BPPV + VD groups, respectively. There was no statistically significant difference ( P > .05) in the NLR, PLR, or MPV between the main patient group or the individual patient subgroups and the control group. Our findings suggest that NLR, PLR, and MPV do not change significantly either in BPPV or in other peripheral vestibular disorders.

For decades, scientists of Almaty Academgorodok research institutes have been conducting enormous research in leading areas of the agro-industrial area producing hundreds of thousands of articles and other documents. However, it should be recognized that the results of these studies remain inaccessible to the vast majority of researchers in the age of the information explosion. One of the reasons for this problem is the lack of a publicly available information repository in the field of agriculture. For this reason, an integrated distributed information system of Academgorodok has been created the main objective of which is not only to preserve the rich heritage of the research institutes, but also to provide access to them and the ability to quickly search for the necessary information. The presented talk describes the architecture of the integrated distributed information system created for storing digitized works of employees of Almaty Akademgorodok research institutes and providing access to them using Web technology. Comparative analysis data storage systems and underlying software for storing digitized works is provided.