bluuebunny/crossref_metadata_2025 huggingface dataset:
Phytoconstituents profiling and antioxidant potential of Wrightia tinctoria R. Br.
Authors: Rajkumar S. , Sathyaprabha G. , Mathanmohun Maghimaa
Published: March 2023

In the Indian traditional system of medicine, Wrightia tinctoria R.Br. (Apocyanaceae) is recognized as a biologically effective therapeutic plant for the treatment of jaundice. It is a natural medicinal tree possessing antidiabetic, anti-inflammatory, hepatoprotective, antinociceptive, antifungal, antibacterial, antipsoriatic, antiviral, anthelmintic, anticancerous, analgesic, antipyretic, and aphrodisiac activities. Methanolic extract of W. tinctoria plant was investigated with Gas Chromatography–Mass Spectrometry (GC-MS), Fourier transform infrared spectroscopy (FTIR) and the antioxidant activity of W. tinctoria was analysed by most probable hydrogen peroxide scavenging (H2O2) activity, DPPH activity and Thiobarbutaric acid. The phytochemical in W. tinctoria leaf and bark have been assessed by GC-MS analysis. GC-MS analysis of W. tinctoria methanolic extract exposed the existence of the GC-MS chromatograms of 10 peaks in the leaf and 20 peaks in the bark. The FTIR spectroscopy analyses were identified by various functional compounds in the extracts with distinctive peak values. The FTIR analysis of methanolic leaf extracts of W. tinctoria confirmed the presence of alcohol, amine, alkane, carboxylic acid, sulfur compounds, halogen compounds and alkyne which showed major peaks. Also the methanolic bark extracts of W. tinctoria confirmed the presence of amines, phenol, alcohols, alkane, aldehydes, carboxylic acid, nitrogen compounds, sulfur compounds, and halogen compounds which also exhibited major peaks. Significant antioxidant activity is displayed by the plant part of leaf and bark sample. The results obtained in the determination of antioxidant activity of MEWT displayed considerable free radical scavenging capacity against DPPH which generated free radicals. This study includes the identification of phytochemicals and antioxidant potential of methanolic and aqueous extract of W. tinctoria which assist in therapeutic claims about this species in the traditional medicinal plant system.
Psoriasiform Spongiotic Dermatitis Drug Eruption following Pfizer-BioNTech SARS-CoV-2 mRNA Vaccine Administration
Authors: Nguyen Kevin , Pham Diem Q. , Erickson Christof P.
Published: March 2023

Introduction: Cutaneous manifestations such as morbilliform rashes, lichen planus, and local injection site patches have been recently published in case reports to occur within days of receiving the coronavirus disease 2019 (COVID-19) vaccine. The most common drug eruptions have been noted to be delayed hypersensitivity reactions. 
Objective: To spotlight a vaccine drug eruption case in a patient with a long history of the autoimmune condition, psoriasis vulgaris.
Case Presentation: A 51-year-old Caucasian female presented with pruritic and erythematous rashes covering her back, abdomen, pelvis, and both upper extremities emerging one week after receiving the Pfizer BioNTech mRNA vaccine. The rashes worsened, rapidly spreading toward the lower extremities within five days after her second dose. The patient was diagnosed with psoriasiform spongiotic dermatitis compatible with a drug eruption and began loratadine and clobetasol cream treatment and phototherapy.
Conclusion: With limited published data available on skin reactions to the COVID-19 vaccine, our case report is among one of the first presentations to describe a morbilliform rash induced by a Pfizer BioNTech mRNA drug-eruption. Although this is a rare case, we may expect more reported drug eruptions to be documented as mass vaccinations continue to be dispensed across the globe. Physicians must be prepared to accurately diagnose and treat dermatologic conditions on patients with and without pre-existing illnesses.
Perspectives on Pediatric Hidradenitis Suppurativa Care: A Survey of Pediatric Providers
Authors: Masson Rahul , Shih Terri , De Devea , Atluri Swetha , Yazdani Shahram , Sayed Christopher , Shi Vivian , Hsiao Jennifer Lin
Published: March 2023

Background:  Hidradenitis suppurativa, or HS, is a chronic, inflammatory skin condition characterized by abscesses, nodules, and fistulas typically in intertriginous areas of the body. Pediatric providers are key front-line providers for children and adolescents with HS, yet little is known about their diagnostic and management approach.
Objective: In this survey study, we elicited the perspectives and experiences of pediatric providers regarding HS care.
Methods: An anonymous survey was distributed to pediatric providers through online pediatric organizational listservs. Survey questions addressed providers’ perspectives on HS diagnosis and management. Comparative statistics between survey responses and provider experience were performed using t-tests and a p-value <0.05 was considered significant.
Results: Among the 50 respondents, less than one-half were confident in knowing the available treatment options for HS (46%), managing mild HS (42%) or moderate-severe HS (6%), knowing pediatric HS comorbidities (30%), addressing challenges that HS patients face in school (22%), knowing when to discuss surgical treatments (20%), managing menstrual HS flares (14%), discussing the impact of HS on sexual health (14%), and managing patients with non-prescription therapies (0%). Of the 25 participants who saw patients with HS, less than two-thirds “often/sometimes” screened for substance abuse (64%), polycystic ovarian syndrome  (60%), premature adrenarche (28%), and inflammatory bowel disease (20%).
Conclusion: Educational resources targeted towards pediatric providers and increased collaboration with dermatologists may improve HS care for children and adolescents.
Petaloid Seborrheic Dermatitis: A Variant Described Primarily in Skin of Color
Authors: Christensen Rachel , Powers Colleen , Mockbee Chelsea , Brodell Robert
Published: March 2023

Petaloid seborrheic dermatitis is a distinct variant of seborrheic dermatitis most commonly affecting patients with skin of color. It is characterized by arcuate coalescing lesions with fine scale and a raised border that symmetrically expands over the course of weeks in a seborrheic distribution.  Two patients with extensive petaloid seborrheic dermatitis of the face are presented who quickly responded to a typical regimen for seborrheic dermatitis.  Recognition of petaloid seborrheic dermatitis will prevent misdiagnosis and improper treatment of this common condition.
A Missed Diagnosis of Alpha-gal Allergy in the Northern United States: A Case Report
Authors: Roster Katie , Mulvihill Hannah , Lakhi Nisha
Published: March 2023

Alpha-gal syndrome is an acquired mammalian meat allergy transmitted via tick bite. Herein, we describe a case of alpha-gal syndrome in the Northern United States that goes unrecognized by multiple healthcare professionals. This case highlights the importance of keeping this diagnosis in mind when treating patients with unexplained urticaria and anaphylaxis.
Durability of Efficacy and Safety of Roflumilast Cream 0.3% in Adults With Chronic Plaque Psoriasis From a 52-Week, Phase 2 Open-Label Safety Trial
Authors: Lebwohl Mark , Stein Gold Linda , Gooderham Melinda , Papp Kim , Ferris Laura , Adam David , Hong H. Chih-ho , Kircik Leon , Zirwas Matthew , Burnett Patrick , Higham Robert , Krupa David , Berk David
Published: March 2023

Background: Roflumilast cream is a potent phosphodiesterase 4 inhibitor recently approved in the United States for treatment of plaque psoriasis with no limitations on duration of use. An open-label trial was conducted to evaluate long-term safety (52 weeks) of once-daily roflumilast cream (NCT03764475). This abstract presents data on durability of response as measured by the percentage of patients with an Investigator Global Assessment (IGA) score of Clear or Almost Clear, percentage improvement in Psoriasis Area Severity Index (PASI) score, and reduction in body surface area (BSA) affected.
Methods: Patients who completed a parent, phase 2b, 12-week randomized controlled trial could continue on open-label roflumilast cream 0.3% (Cohort-1, n=230), and patients naïve to roflumilast were also enrolled (Cohort-2, n=102). All psoriasis lesions (except scalp) were treated, including face and intertriginous areas for up to 52 weeks. If affected, palms and soles were treated, but not evaluated towards any efficacy assessments. Median duration of response was determined using the Kaplan-Meier method.
Results: With cumulative treatment up to 64 weeks in Cohort-1 and 52 weeks in Cohort-2, long-term safety and tolerability were consistent with the 12-week, phase 2b study. Overall, 73.5% of patients completed the study; 3.9% discontinued due to adverse events (AE) and 0.9% discontinued due to lack of efficacy. Treatment-related AEs were reported in 2.7% patients; none were deemed serious. Investigator tolerability assessments at each visit demonstrated 99% of patients rated “no evidence of irritation.” At Week 52, IGA Success (demonstrating Clear/Almost Clear plus 2-grade improvement from baseline) was achieved by 34.8% of patients in Cohort-1 and 39.5% in Cohort-2. Of patients in Cohort-2, 40% of patients achieved IGA success at week 12. IGA Clear/Almost Clear was achieved by 46.8% of patients across both cohorts at week 12 and consistent through week 52 (44.8%). Similarly, a 60.5% mean PASI improvement and 60.1% mean BSA improvement from baseline were observed at week 12 and consistent through week 52 (59.4% and 63.3%, respectively). Of the 185 patients who achieved IGA Clear/Almost Clear during the open-label trial, the median durability of IGA of Clear/Almost Clear was 10 months (40.1 weeks). Among patients who achieved an IGA of Clear or Almost Clear, 50% maintained Clear or Almost Clear status for at least 10 months.
Conclusions: In this long-term safety study, roflumilast cream was well tolerated with a safety profile consistent with the parent Ph2b trial, and effectively maintained clear/almost clear skin with no tachyphylaxis observed.
Sponsored by Arcutis Biotherapeutics, Inc.
Acne symptoms and impact of acne on social functioning, emotional functioning, and activities of daily living (ADL) among pediatric patients with moderate to severe non-nodular Acne Vulgaris (AV) in community practices across the U.S: PROSES study
Authors: Hebert Adelaide , Rieder Evan , Graber Emmy , Baldwin Hilary , Harper Julie , Stein Gold Linda , Kircik Leon , Alexis Andrew , Del Rosso James , Narayanan Siva , Koscielny Volker , Kasujee Ismail , Fried Richard
Published: March 2023

Objective: Evaluate patient self-perceived AV symptoms and impact of AV on emotional/social functioning and ADL, among pediatric patients with AV in community practices across the U.S. Methods: Single-arm, prospective cohort study (PROSES) was conducted with moderate-to-severe non-nodular AV patients >9yrs who were prescribed sarecycline in real-world U.S community practices. Validated ASIS questionnaire (with Signs and Impact (emotional & social) domains) and an Expert Panel Questionnaire (EPQ; emotional functioning (items 1-4), social functioning (items 5-7), and ADL (items 8-11)) were completed by patients (>12yrs) and caregivers (for patients 9-11yrs) at baseline and week-12. All items were scored on five-point adjectival response scale (score: 0 (no burden/impact) – 4 (most burden/impact)); a higher ASIS domain score indicate severe symptoms or negative impact of AV. ASIS domain scores and proportion of patients reporting score=2/3/4 (moderate to high burden/impact) for EPQ items at baseline for pediatric age strata (Grp1: age 9-11yrs, Grp2: age 12-17yrs) was analyzed. Results: A total of 101 pediatric patients with AV were included in the analysis (mean age: 14.81yrs; age Grp1: 3.96%, age Grp2: 96.04%; female: 49.50%; white/Caucasian: 78.22%; Hispanic/Latino/Spanish origin: 30.69%). At baseline, patients reported moderate AV burden in most domains, as depicted by: signs domain scores of Grp1: 2.00, Grp2: 1.92; emotional impact subdomain scores of Grp1: 2.00, Grp2: 2.02; social impact subdomain scores of Grp1: 0.25, Grp2: 0.28. From EPQ items, proportion of patients reporting score=2/3/4 (moderate to severe burden) within age strata at baseline were: patients’ mood/anger (EPQ1)- Grp1: 25.00%, Grp2: 41.24%; worries about AV worsening (EPQ2)- Grp1: 50.00%, Grp2: 74.23%; thinking about acne (EPQ3)- Grp1: 50.00%, Grp2: 75.26%; level of acne worries (EPQ4)- Grp1: 50.00%, Grp2: 64.95%; patients’ social media/’selfie’ activity (EPQ5)- Grp1: 50.00%, Grp2: 37.11%; impact on real-life plans (EPQ6)- Grp1: 25.00%, Grp2: 27.84%; efforts to hide AV (EPQ7)- Grp1: 75.00%, Grp2: 63.92%; picked-on/judged due to AV (EPQ8)- Grp1: 25.00%, Grp2: 26.80%; ability to reach future goals (EPQ9)- Grp1: 25.00%, Grp2: 16.49%; parent understanding of AV concerns (EPQ10)- Grp1: 75.00%, Grp2: 82.47%; sleep impact (EPQ11)- Grp1: 50.00%, Grp2: 20.62%. Conclusion: Moderate to severe AV burden and psychosocial impact was observed in this prospective cohort of pediatric patients with AV in the U.S. Emotional impact and social impact of AV were more pronounced across the pediatric age groups.
Antenatal diagnosis of Sirenomelia, the Mermaid syndrome with bilateral renal agenesis
Authors: Rani Ankita , Sultan Moinuddin
Published: March 2023

A 26-year-old non-diabetic primigravida with 4 months of amenorrhea was appointed for a routine second-trimester anomaly scan. On inspection, the gravid abdominal girth of the lady did not correlate with her gestational age. Ultrasonographic examination showed a single live intrauterine gestation with anhydramnios. There was an absence of bilateral kidneys and urinary bladder with lying down adrenal sign suggestive of bilateral renal agenesis. The fetus also revealed caudal dysgenesis in the form of fusion of both lower limbs, seen as a single leg with 1 upturned foot and fused toes. There were no identifiable external genitalia and anus. The parents went ahead with medical termination of pregnancy after being informed about the condition and its incompatibility with life.
Endovascular embolization of inferior pancreaticoduodenal artery pseudoaneurysm post-laparoscopic cholecystectomy in a patient with celiac artery stenosis – A case report
Authors: Vignesh S. , Mukuntharajan T.
Published: March 2023

Inferior pancreaticoduodenal artery (iPDA) pseudoaneurysms are mostly secondary to pancreatitis, abdominal trauma, or iatrogenic procedures. We present a rare case of iPDA pseudoaneurysm secondary to laparoscopic cholecystectomy in a patient with celiac artery stenosis. A 50-year-old man who underwent laparoscopic cholecystectomy 7 days back presented with abdominal pain, blood in drain output, and tachycardia. Abdominal computed tomography (CT) showed a large retroperitoneal hematoma adjacent to head of pancreas with a pseudoaneurysm likely arising from gastroduodenal artery. Proximal stenosis of celiac artery was also present. Digital subtraction angiography (DSA) showed pseudoaneurysm arising from posterior branch of iPDA. Coil embolization was performed with complete obliteration of the aneurysm. However, the patient presented again with increasing abdominal pain and hemoglobin drop after 8 days. CT showed migration of coil loop into the hematoma and residual filling of pseudoaneurysm. Repeat embolization was planned and the pseudoaneurysm with iPDA branch was embolized with 33% glue-lipoidal mixture. On follow-up 3 months later, the patient was found to be stable with no further complications. iPDA pseudoaneurysm is less commonly encountered visceral artery pseudoaneurysm. Trapping of pseudoaneurysm with both proximal and distal vessel occlusion is ideal method for embolization to prevent recurrence.
Imaging of bilateral tendoachilles xanthomatosis in a young woman
Authors: Devi Suba Arul , Machaiah K. M. , Pinto Amanda C. , Rai Santosh P. V.
Published: March 2023

Bilateral tendoachilles xanthomatosis is a rare entity and is frequently found in association with the primary hyperlipidemia. It is characterized by the deposition of cholesterol in tendons. An early diagnosis with different imaging modalities changes the course of the disease. This case report illustrates the bilateral tendoachilles xanthomas on MRI imaging in a patient who presented with painless progressive swelling of bilateral ankle joints for several years. Intralesional subtotal resection was successfully done and histological evaluation further confirmed the diagnosis.
Acrorenal ocular syndrome: Case series of a rare familial congenital syndrome
Authors: Ganesh Rajagopal , Jayanthan S. Shanmuga , Karunakaran N. , Rupesh G. , Nadanasadharam K. , Dande Sidramappa
Published: March 2023

Acrorenal ocular syndrome includes a spectrum of acral anomalies such as oligodactyly, ectrodactyly, syndactyly, brachydactyly, humerus/carpal hypoplasia, cutaneous syndactyly, and renal anomalies such as unilateral renal agenesis, unilateral hypoplasia, ectopia, horseshoe kidney, and vesico-ureteric reflex. The common ocular manifestations include Duane anomaly, coloboma, and ptosis.
Duodenal intussusception due to periampullary duodenal adenoma: A case report
Authors: Chawla Siddhi , Charan Aditya , Joshi Ashish , Sihag Dharam Veer
Published: March 2023

Duodenal intussusceptions are uncommon due to their fixed location in retroperitoneum except when associated with bowel malrotation abnormalities. We present a case of recurrent duodenojejunal intussusception in a 34-year-old female diagnosed on imaging. The lead point, in our case, was periampullary duodenal tubulovillous adenoma which was confirmed on endoscopy and subsequent punch biopsy. The patient underwent segmental duodenal resection anastomosis preserving the ampulla with reduction of the intussuceptum and fixation of the jejunal loops and its mesentery.
A MATHEMATICAL MODEL OF FREEZING OF UNSATURATED SOILS IN THE PRESENCE OF CAPILLARY PRESSURE
Authors: Цыпкин Г.Г.
Published: March 2023

Сформулирована математическая модель промерзания грунта, насыщенного гетерогенной смесью воды и воздуха, при наличии капиллярного давления. Представлен вывод уравнения диффузии влаги, следующий из законов сохранения масс и импульса, позволяющий выразить коэффициент диффузии через параметры среды. Выведены балансовые соотношения и предложено замыкающее соотношение на фронте кристаллизации воды. В линейном приближении получено автомодельное решение задачи.

A mathematical model of freezing of soils saturated with a heterogeneous mixture of water and air in the presence of capillary pressure is proposed. The derivation of the diffusion equation for the redistribution of moisture from the laws of conservation of mass and momentum is given. This allows us to define the diffusion coefficient through the parameters of the porous medium and fluids. Balance relations through the water crystallization front is derived. A self-similar solution of the problem in the linear approximation is obtained. It is shown that the growth of capillary forces reduces the amount of ice formed, and a more intensive freezing regime leads to an increase in the saturation with ice.
ON RELATIVE BOUNDEDNESS OF A CLASS OF DEGENERATE DIFFERENTIAL OPERATORS IN THE LEBESGUE SPACE
Authors: Исхоков Ф.С. , Гадоев М.Г.
Published: March 2023

В пространстве Lp(Ω), где 1 < p < +∞ иΩ  – произвольная (ограниченная или неограниченная) область n-мерного евклидова пространства Rn, исследуется относительная ограниченность одного класса дифференциальных операторов с частными производными недивергентного вида высшего порядка. Исследуемые операторы имеют нестепенное вырождение вдоль всей границы области Ω, и вырождение по каждой независимой переменной характеризуется с помощью разных функций. В работах, опубликованных ранее по этому направлению, обычно сначала задавался исследуемый оператор в области  и затем в этой области определялись функции, с помощью которых характеризуются вырождения коэффициентов исследуемого оператора. Эти функции имели одинаковое поведение вблизи границы по разным независимым переменным. В отличие от этого, в настоящей работе область Ω и функции, которые характеризуют вырождения коэффициентов дифференциального оператора, задаются в паре друг с другом и предполагается выполнение «условия погружения», введенного ранее П. И. Лизоркиным. При этом дифференцируемость функций, с помощью которых определяется вырождение исследуемого оператора, не требуется. Исследование относительной ограниченности дифференциальных операторов является одним из основных направлений теории таких операторов, и результаты, полученные в этом направлении, имеют широкое применение в теории вложения нормированных пространств дифференцируемых функций многих переменных, теории разделимости дифференциальных операторов, спектральной теории дифференциальных операторов и т.д.

In the space Lp(Ω), where 1 < p < +∞ and  is an arbitrary (bounded or unbounded) domain in Rn, we investigate relative boundedness for a class of higher order partial differential operators in non-divergent form. These operators have nonpower degeneracy on the whole boundary of Ω and degeneracy with respect to each of independent variables is characterized by different functions. In the earlier published papers in this direction, as a rule, firstly the operator is defined in Ω and then functions characterizing degeneracies of the operator’s coefficients are defined in this domain. In contrast to that, here we define Ω and these functions related to each other while fulfilling the “immersion condition” introduced by P. I. Lizorkin in [19]. In addition, differentiability of the functions by which we define degeneracy of the investigated operator is not required. Study of relative boundedness of differential operators is one of the modern directions in such operators theory with results theory of differentiable functions of many variables, the separation theory of differential operators, the spectral theory of differential operators, etc.
ON JUNCTION PROBLEM FOR ELASTIC TIMOSHENKO INCLUSION AND SEMI–RIGID INCLUSION
Authors: Хлуднев А.М. , Попова Т.С.
Published: March 2023

Исследуется краевая задача, описывающая равновесие двумерного упругого тела с двумя тонкими сопрягающимися включениями при наличии отслоения. При этом одно из включений является упругим, а другое – полужестким. Наличие отслоения означает существование трещины между включениями и упругим телом. На берегах трещины задаются нелинейные краевые условия вида неравенств, которые не позволяют противоположным берегам трещин проникать друг в друга. Указанные краевые условия приводят к формулировке проблемы в виде задачи с неизвестным множеством контакта. Приведена как дифференциальная постановка в виде краевой задачи, так и вариационная постановка в виде задачи минимизации функционала энергии на выпуклом множестве допустимых перемещений. Обоснована однозначная разрешимость поставленной задачи. Показана эквивалентность дифференциальной и вариационной постановок. Исследован предельный переход по параметру жесткости тонкого упругого включения. Найдены условия сопряжения как для исходной задачи, так и для предельной.

An equilibrium problem for elastic bodies with a thin elastic inclusion and a thin semi-rigid inclusion is investigated. The inclusions are assumed to be delaminated from the elastic bodies, forming therefore a crack between the inclusions and the elastic matrix. Nonlinear boundary conditions are considered at the crack faces to prevent mutual penetration between the crack faces. The inclusions have a joint point. We present both differential formulation in the form of a boundary value problem and a variational formulation in the form of a minimization problem for an energy functional on a convex set of admissible displacements. The unique solvability of the problem is substantiated. Equivalence of differential and variational statements is shown. Passage to the limit is investigated as the rigidity parameter of the elastic inclusion goes to infinity. The limit model is analyzed. Junction boundary conditions are found at the joint point for the considered problem as well as for the limit problem.
ON THE BASICS OF COMMON THEORY FOR COORDINATION POLYHEDRON COMPOSITION (POLYHEDRON FUNDAMENTAL EQUATIONS)
Authors: Петрушко М.И.
Published: March 2023

Рассматриваются особенности геометрического строения многогранников, связанных с их принадлежностью к различным группам симметрии. Выводятся основные уравнения для вершин, граней и ребер многогранников в зависимости от их расположения на аксиальных, планарных и примитивных орбитах.

We study the features of the polyhedron geometric structure related to their belonging to different symmetry groups. We derive basic equations for the vertices, faces, and edges of the polyhedron depending on their location on the axial, planar, and primitive orbits.
ITERATIVE METHOD FOR THE DIRICHLET PROBLEM AND ITS MODIFICATIONS
Authors: Васильев В.И. , Кардашевский А.М. , Попов В.В.
Published: March 2023

Исследованию существования, единственности и численным методам решения обратной задачи Дирихле для гиперболических уравнений второго порядка посвящен цикл работ научной школы член-корреспондента РАН С. И. Кабанихина. В данной работе рассматривается численное решение неклассической задачи Дирихле и ее модификаций для двумерного гиперболического уравнения второго порядка. Применяется метод итерационного уточнения недостающего начального условия с помощью дополнительного условия, заданного в конечный момент времени. При этом на каждой итерации численно реализуется прямая задача. Эффективность предлагаемого вычислительного алгоритма подтверждена расчетами для модельных двумерных задач, в том числе при задании дополнительных условий со случайными ошибками.

A series of works of S. I. Kabanikhin’s scientific school are devoted to study of the existence, uniqueness, and numerical methods for the inverse Dirichlet problem for the second-order hyperbolic equations. We consider a numerical solution to the non-classical Dirichlet problem and its modifications for the two-dimensional hyperbolic second-order equations. The method of iterative refinement of the missing initial condition is applied by means of an additional condition specified at the final time. Moreover, the direct problem is numerically realized at each iteration. The efficiency of the proposed computational algorithm is confirmed by calculations for two-dimensional model problems, including additional conditions with random errors.
SIMULATION OF FILTRATION PROBLEMS IN FRACTURED POROUS MEDIA WITH MIXED FINITE ELEMENT METHOD (EMBEDDED FRACTURE MODEL)
Authors: Спиридонов Д.А. , Васильева М.В.
Published: March 2023

Представлена математическая модель смешанной размерности течения жидкости в трещиноватых пористых средах (встроенная модель трещин). Математическая модель описывается системой параболических уравнений: d-размерной для пористой среды и (d-1)-размерной для системы трещин. Система уравнений связана посредством задания специальной функции перетока. Данная модель позволяет использовать сетки для матрицы пористой среды, не зависящие от сетки для трещин. Для численного решения строится аппроксимация с использованием смешанного метода конечных элементов. Представлены результаты численного решения модельной задачи, которые показывают работоспособность предложенного метода для моделирования течения в трещиноватых пористых средах.

We present a mathematical model of mixed dimension for modeling filtration problems in fractured porous media (built-in model of cracks). The mathematical model is described by a system of parabolic equations: d-dimensional for a porous medium and (d - 1)-dimensional for a system of cracks. The system of equations is connected by specifying a special flow function. This model allows the use of grids for a matrix of a porous medium not dependent on the grid for cracks. For the numerical solution, an approximation using the mixed finite element method is constructed. The results of the numerical solution of the model problem that show the operability of the proposed method for modeling the flow in fractured porous media are presented.
On the second boundary value problem for nonstationary third-order equations of mixed type
Authors: Khashimov A.
Published: March 2023

Рассмотрена вторая краевая задача для нестационарного уравнения третьего порядка составного типа. Исследованы асимптотические свойства фундаментальных решений уравнения, использованные при построении регулярных решений краевых задач.

We consider the second boundary value problem for nonstationary third-order equations of mixed type. and study asymptotic characteristics of fundamental solutions of the equations, which are used for constructing of regular solutions to the boundary value problems.
Euler type differential equations of fractional order
Authors: Жуковская Н.В. , Ситник С.М.
Published: March 2023

Дано решение неоднородного дифференциального уравнения типа Эйлера с дробными производными Римана – Лиувилля на полуоси в классе функций, представимых дробным интегралом, в терминах дробного аналога функции Грина. Построены дробные аналоги функции Грина в том случае, когда все корни характеристического многочлена различны, а также в случае, когда среди корней характеристического многочлена есть кратные. Сформулированы и доказаны теоремы разрешимости неоднородного дробно-дифференциального уравнения типа Эйлера на полуоси. Рассмотрены некоторые частные случаи и примеры.
Weyl-almost periodic and asymptotically Weyl-almost periodic properties of solutions to linear and semilinear abstract Volterra integro-differential equations
Authors: Kostic M
Published: March 2023

The main purpose of paper is to consider Weyl-almost periodic and asymptotically Weyl-almost periodic solutions of linear and semilinear abstract Volterra integro-differential equations. We focus our attention to the investigations of Weyl-almost periodic and asymptotically Weyl-almost periodic properties of both, finite and infinite convolution product, working in the setting of complex Banach spaces. We introduce the class of asymptotically (equi)-Weyl-p-almost periodic functions depending on two parametres and prove a composition principle for the class of asymptotically equi-Weylp-almost periodic functions. Basically, our results are applicable in any situations where the variation of parameters formula takes a role. We provide several new contributions to abstract linear and semilinear Cauchy problems, including equations with the Weyl Liouville fractional derivatives and the Caputo fractional derivatives. We provide some applications of our abstract theoretical results at the end of paper, considering primarily abstract degenerate differential equations, including the famous Poisson heat equation and its fractional analogues.
Singular Cauchy problem for generalized homogeneous Euler-Poisson-Darboux equation
Authors: Shishkina E. , Karabacak M.
Published: March 2023

In this paper, we solve singular Cauchy problem for a generalised form of an homogeneous Euler–Poisson–Darboux equation with constant potential, where Bessel operator acts instead of the each second derivative. In the classical formulation, the Cauchy problem for this equation is not correct. However, S. A. Tersenov observed that, considering the form of a general solution of the classical Euler–Poisson–Darboux equation, the derivative in the second initial condition must be multiplied by a power function whose degree is equal to the index of the Bessel operator acting on the time variable. The first initial condition remains in the usual formulation. With the chosen form of the initial conditions, the considering equation has a solution. Obtained solution is represented as the sum of two terms. The first tern is an integral containing the normalized Bessel function and the weighted spherical mean. The second term is expressed in terms of the derivative of the square of the time variable from the integral, which is similar in structure to the first term.
MIXED MULTISCALE FINITE ELEMENT METHOD FOR PROBLEMS IN PERFORATED MEDIA WITH INHOMOGENEOUS DIRICHLET BOUNDARY CONDITIONS
Authors: Васильева М.В. , Спиридонов Д.А. , Эфендиев Я. , Чун Э.Т.
Published: March 2023

Рассматривается решение эллиптического уравнения в смешанной постановке в перфорированной среде с неоднородными граничными условиями Дирихле на границе перфораций. Для решения задачи на мелкой сетке (эталонное решение) используется смешанный метод конечных элементов (Mixed FEM), где аппроксимация скорости реализована с помощью элементов Равиарта — Томаса наименьшего порядка и кусочно постоянных базисных функций для давления. Решение на грубой сетке выполнено с использованием смешанного обобщенного многомасштабного метода конечных элементов (Mixed GMsFEM). Поскольку перфорации оказывают огромное влияние на процессы в среде, то возникает необходимость вычисления дополнительного базиса, учитывающего влияние перфораций на решение задачи. Приводятся результаты численного эксперимента в двумерной области, подтверждающие работоспособность предложенного многомасштабного метода.
Computational experiment for identifying of cubic period of hexagonal diamond
Authors: Ерёмин И.Е. , Фомин Д.В.
Published: March 2023

The coefficient of compactness and the Madelung constant are key parameters in researches of substances in condensed state. The method of compact matrix description of crystal lattice makes calculation of these parameters faster and simpler. However, since this method is based on cubic symmetry of the crystal structure, it cannot be applied to substances of noncubic syngony. In this paper, we study the crystal lattice of a hexagonal diamond to determine existence of the cubic period and cube-generator. The goals of our study are the following: 1) to determine the presence or absence of the cubic period and cube-generator of the crystal lattice; 2) to determine the space orientation of the cube-generator; 3) to determine the value of the cubic period; 4) to verify preservation of the discovered periodicity for an extensive crystal fragment. The results of the computational experiment prove the existence of the cubic period and cube-generator. The value of the cubic period is obtaine (36 notational units, ∼ 2, 14 nm). Its preservation for an extensive crystal fragment is shown. It is shown that the space orientation of the cube-generator and basic elements of a two-component cubic model of the crystal lattice of the hexagonal diamond is the same. The obtained results lead to applicability of the method of compact matrix description to the crystal lattice of the hexagonal diamond, thus optimizing the calculation of the compactness coefficient and the Madelung constant for this substance.
PSEUDOPARABOLIC AND PSEUDOHYPERBOLIC EQUATIONS IN NONCYLINDRICAL TIME DOMAINS
Authors: Кожанов А.И. , Лукина Г.А.
Published: March 2023

Исследована разрешимость новых краевых задач для псевдопараболических и псевдогиперболических дифференциальных уравнений с одной пространственной переменной. Отличительной особенностью этих задач является то, что их решения ищутся в нецилиндрических по временной переменной областях, а не в областях с криволинейными боковыми сторонами (областях с подвижной границей), как в других работах. Для изучаемых задач доказываются теоремы существования и единственности регулярных (имеющих во внутренних подобластях все обобщенные по С. Л. Соболеву производные, входящие в уравнение) решений.

We study solvability of new boundary value problems for pseudoparabolic and pseudohyperbolic equations with one spatial variable. The solutions for these problems are sought in domains noncylindrical along the time variable, not in the domains with curvilinear borders (domains with moving border) as in the previous works. We prove the existence and uniqueness theorems for the regular solutions, those having all generalized Sobolev derivatives, required in the equation, in the inner subdomains.
DIFFERENTIATION OF THE ENERGY FUNCTIONALS FOR EQUILIBRIUM PROBLEMS OF THE KIRCHHOFF–LOVE PLATES WITH NONPENETRATION CONDITIONS FOR KNOWN CONFIGURATIONS OF PLATE EDGES
Authors: Лазарев Н.П. , Григорьев М.П.
Published: March 2023

Рассматриваются вариационные задачи теории упругости в области с разрезом, описывающие равновесие пластины с трещиной. Предполагается, что под действием определенных заданных нагрузок пластина имеет деформации с определенной заранее известной конфигурацией кромок вблизи трещины. На кривой в срединной плоскости, соответствующей трещине, заданы краевые условия в виде двух неравенств. В предположении, что параметр описывает возмущение трещины, находится производная функционала энергии по отношению к . Результаты получены для новых математических моделей с новыми краевыми условиями, описывающими специальный характер контактного взаимодействия кромок пластины.

Equilibrium problems for elastic plates with a rectilinear crack are studied. It is assumed that under the action of certain given loads, plates have deformations with a certain predetermined configuration of edges near the crack. On the crack curve, we impose a nonlinear boundary condition as an inequality describing the nonpenetration of the opposite crack faces. Assuming that the parameter describes the crack perturbation, the derivative of the energy functional with respect to is found. The results are obtained for new mathematical models with new nonlinear boundary conditions describing special character of the mechanical contact interaction of the plate edges.
BOUNDARY CONTROL FOR PSEUDOPARABOLIC EQUATIONS IN SPACE
Authors: Fayazova Z.
Published: March 2023

Let u(x, y, t) be a solution to the pseudoparabolic equation that satisfies the initial and boundary conditions. The value of the solution is given on the part of boundary of the considered region which contains the control parameter. It is required to choose the control parameter so that on a part of the regularity domain the solution takes the specified mean value. First, we consider an auxiliary boundary value problem for a pseudoparabolic equation. We prove the existence and uniqueness of the generalized solution from the corresponding class. The restriction for the admissible control is given in the integral form. By the separation variables method, the desired problem is reduced to the Volterra integral equation. The latter is solved by the Laplace transform method. The theorem on the existence of an admissible control is proved.
ASYMPTOTIC PROPERTIES OF SOLUTIONS IN A MODEL OF INTERACTION OF POPULATIONS WITH SEVERAL DELAYS
Authors: Скворцова М.А.
Published: March 2023

Рассматривается модель, описывающая взаимодействие n видов микроорганизмов. Модель представлена в виде системы нелинейных дифференциальных уравнений с несколькими постоянными запаздываниями. Компоненты решений системы отвечают за численности популяций i-го вида и за концентрацию питательного вещества. Параметры запаздывания обозначают время, необходимое для появления i-го вида после потребления питательного вещества. Изучаются асимптотические свойства решений рассматриваемой системы. При определенных условиях на параметры системы получены оценки для всех компонент решений. Установленные оценки характеризуют скорости убывания численностей популяций микроорганизмов и скорость стабилизации концентрации питательного вещества к начальной величине концентрации. Оценки имеют конструктивный характер, все величины, характеризующие скорости стабилизации, указаны в явном виде. При получении оценок были использованы модифицированные функционалы Ляпунова Красовского.

We consider a model describing the interaction of n species of microorganisms. The model is presented as a system of nonlinear differential equations with several constant delays. The components of solutions to the system are responsible for the biomass of the i-th species and for the concentration of the nutrient. The delay parameters denote the time required for the conversion of the nutrient to viable biomass for the i-th species. In the paper, we study asymptotic properties of the solutions to the considered system. Under certain conditions on the system parameters, we obtain estimates for all components of the solutions. The established estimates characterize the rate of decrease in the biomass of microorganisms and the rate of stabilization of the nutrient concentration to the initial value of the concentration. The estimates are constructive and all values characterizing the stabilization rate are indicated explicitly. The modified LyapunovKrasovskii functionals were used to obtain the estimates.
SOME BOUNDARY VALUE PROBLEMS FOR THE SOBOLEV–TYPE OPERATOR–DIFFERENTIAL EQUATIONS
Authors: Уварова М.В. , Пятков С.Г.
Published: March 2023

Рассматривается вопрос о разрешимости краевых задач для операторнодифференциального уравнения вида But Lu f, где B, L : X X (X банахово пространство) замкнутые операторы такие, что D(L) D(B) (D(L), D(B) области определения соответствующих операторов), с краевыми условиями Bu(0) Bu0 или TR0 Bu()d() Bu0, где функция ограниченной вариации. Уточняются некоторые известные результаты о разрешимости начальнокраевых задач для операторнодифференциальных уравнений типа Соболева в случае произвольного убывания (роста) резольвенты соответствующего линейного пучка. Получены теоремы о существовании и единственности решений задачи типа Коши и нелокальной краевой задачи общего вида, в том числе при определенных условиях показана максимальная регулярность решений. Последние результаты основаны на теореме Михлина для операторнозначных мультипликаторах Фурье. В отличие от предыдущих результатов в качестве функциональных пространств используются пространства Соболева Бесова.

We consider the solvability of boundary value problems for operatordifferential equation of the form But Lu f, where X is a Banach space, B, L : X X are closed operators such that D(L) D(B) (D(L), D(B) are domains of the corresponding operators), with boundary conditions Bu(0) Bu0 or R0T Bu()d() Bu0, where is a function of bounded variation. Some wellknown results on solvability of initial boundary value problems for operatordifferential equations of Sobolev type are refined in the case of arbitrary decrease (growth) of the resolvent of the corresponding linear pencil. Existence and uniqueness theorems of solutions to the Cauchytype problems and general nonlocal boundary value problems are obtained and the maximal regularity of solutions is proven under certain conditions. The results rely on Mikhlin theorems for operatorvalued Fourier multipliers. In contrast to the previous results, the function spaces are the Sobolev Besov spaces.
ε–RETRACTS, Q–MANIFOLDS, AND FIXED POINTS
Authors: Черников П.В.
Published: March 2023

Приводится обобщение одной теоремы Ногуши о неподвижной точке. Доказано, что существует компактное нестягиваемое ацикличное Qмногообразие, обладающее свойством неподвижной точки. Вводится и изучается понятие топологического пространства, обладающего свойством неподвижной точки. Приведен пример некомпактного множества на плоскости R2, обладающего свойством неподвижной точки.

A generalization of one of the Noguchi fixed point theorems is presented. We prove that there exists a compact noncollapsible acyclic Qmanifold with the fixed point property. A topological space with the fixed point property is introduced and studied and an example of a noncompact set in R2 with the fixed point property is given.
On one application of the Zygmund–Marcinkiewicz theorem
Authors: Kukushkin M.V.
Published: March 2023

In this paper we aim to generalize results obtained in the framework of fractional calculus due to reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained technique on practical problems connected with various physical and chemical processes. More precisely, a class of existence and uniqueness theorems is covered, the most remarkable representative of which is the existence and uniqueness theorem for the Abel equation in a weighted Lebesgue space. The method of proof corresponding to the uniqueness part is worth noticing separately: it reveals properties of the operator as well as properties of the space into which it acts and emphasizes their relationship.
Numerical homogenization for heat transfer problems in the permafrost zone
Authors: Алексеев В.Н. , Тырылгин А.А. , Васильева М.В. , Васильев В.И.
Published: March 2023

В работе рассматриваются задачи теплопереноса с учетом фазовых переходов влаги в промерзающем/протаивающем грунте. Математическая модель процессов теплопереноса с фазовым переходом описывается классической моделью Стефана и представляет собой нелинейное параболическое уравнение. Для решения задачи предложен метод численного усреднения для нелинейной задачи с использованием эффективных коэффициентов теплопроводности и объемной теплоемкости для талой и мерзлой зон. Вычисления эффективного тензора теплопроводности проводится в локальных областях (ячейки грубой сетки) и используются при построении аппроксимации на грубой сетке методом конечных элементов. Численная реализация конечно-элементной аппроксимации проведена с помощью вычислительной библиотеки FEniCS. Представлены численные результаты для двумерной и трехмерной модельных задач.

The work considers heat transfer problems taking into account phase transitions of moisture in the soil. The mathematical model of heat transfer processes with phase transition is described using the classical Stefan model and is a nonlinear parabolic equation. To solve the problem, a numerical homogenization method is proposed for the nonlinear problem using the effective thermal conductivity coefficient for thawed and frozen zones. The calculation of the effective thermal conductivity tensor is carried out in local domains (coarse mesh cells) and is used to construct the approximation on a coarse mesh by the finite element method. Numerical implementation was carried out using FEniCS computational library for finite element approximation. Numerical results are presented for the model problem in two-dimensional and three-dimensional formulations.