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Well-Posedness and Blow-Up of Solutions for a Variable Exponent Nonlinear Petrovsky Equation

Ercan ÇELİK

Article | 2023 | Advances in Mathematical Physics2023

In this article, we investigate a nonlinear Petrovsky equation with variable exponent and damping terms. First, we establish the local existence using the Faedo-Galerkin approximation method under the conditions of positive initial energy and appropriate constraints on the variable exponents p & sdot; and q & sdot;. Finally, we prove a finite-time blow-up result for negative initial energy. Keyword: global existence; wave-equation

Ecology and Environmental Aspects of “Makmalzoloto” Gold Mining Area in Kyrgyzstan

Nazgül İMANBERDİYEVA

Chapter of Books | 2018 | Vegetation of Central Asia and Environs ( Chapter 13 )

This investigation enlightens the original data on the ecological situation of Makmal Valley and neighboring villages Makmal and Chetbulak Toguz-Toro in “Makmalzoloto” gold mining area in Kyrgyzstan. The study was undertaken to put forward the possibilities for preservation of rich biodiversity and ecological state in these villages. The area is under pressure from the activities of gold extraction. Even today environmental pollution and high levels of radiation are observed. The extraction activity has seriously damaged and produced a negative impact on pastures, livestock, as well as biodiversity in this region. The dosimetric stu . . .dies have revealed that in the village Chetbulak, radiation levels lie around 38–40 mcR/h. Since the first extraction from the plant, the tailing pond is lying in the open with no protection or warning signs. The cattle grazes in the area openly all year-round; children lead the cattle herds and play freely around the tailing pond More less

On The Recursive Sequence x(n+1)=x(n-20)/[1+x(n-2)x(n-5)x(n-8)x(n-11)x(n-14)x(n-17)]

Burak OĞUL

Article | 2019 | MANAS Journal of Engineering (MJEN)7 ( 2 )

The behaivour of the solutions of the following system of difference equations is examined, x(n+1)=x(n-20)/[1+x(n-2)x(n-5)x(n-8)x(n-11)x(n-14)x(n-17)] where the initial conditions are positive real numbers. The initial conditions of the equation are arbitrary positive real numbers. Also, we discuss and illustrate the stability of the solutions in the neighborhood of the critical points and the periodicity of the considered equations

Поясное распределение растительности бассейна реки Ат-Баши внутреннего Тянь-Шаня Кыргызстана

Nazgül İMANBERDİYEVA

Article | 2019 | Вестник Удмуртского университета. Серия Биология. Науки о Земле29 ( 2 )

Приводится геоботаническая характеристика основных типов, подтипов, формаций и групп ассоциаций растительности в разрезе высотного профиля. Кыргызстан - высокогорная страна Средней Азии, которая находится в центре горных систем Тянь-Шаня и Памиро-Алая. До 90 % ее территории подняты на абсолютные высоты более 1500 м. Растительный покров Кыргызстана располагается системой вертикальных поясов. В бассейне р. Ат-Баши наиболее широко распространены степи и лугостепи. Среди них различают мелкодерновинные степи и лугостепи, сухие степи и лугостепи со значительной долей полыней и засухоустойчивого разнотравья, также горные луга. Среди горных . . . лугов различают высокотравные, среднетравные и низкотравные. Высокотравные луга, развитые в низкогорьях и среднегорьях, на севере и юге различаются по видовому составу растений. В северных районах ведущее значение имеют виды: Dactylis glomerata, Bromus inermis, Elytrigia repens, Brachypodium pinnatum ; представители родов: Poa, Vicia, Thalictrum . Наибольшая доля в растительном покрове степей принадлежит растениям, которые по требованиям к теплу и влаге занимают промежуточное положение между растениями пустынь и лугов. Основу растительности степей составляют виды родов дерновинных злаков: Stipa, Festuca , Ptilagrostis с очень характерными для них волосовидными и сизоватыми листьями. Степям, в отличие от пустынь и полупустынь, свойственно большее богатство видового состава растений и плотность растительного покрова. Степи служат хорошими пастбищам More less

Determination of some trace elements in various lichens as biomonitors of pollution and assessment of pollution status

Ali ASLAN

Article | 2023 | Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi12 ( 3 )

Some trace elements in various lichens as biomonitors of pollution were investigated. Also, the pollution status was assessed by enrichment factor, contamination factor, and pollution load index. Investigated elements were Ta, Bi, Hf, Nb, Ga, Sc, Li, Y, Ce, and Sr. The lichen species were Rhizoplaca chrysoleuca, Umbilicaria vellea, Aspicilia calcarea, Pseudevernia furfuracea, and Cetraria islandica. According to the results, lichen species accumulate Sr element well. The highest trace element accumulated by Pseudevernia furfuracea (21.7±1.0 mg/kg; 75), Rhizoplaca chrysoleuca (31.9±1.6 mg/kg; 61), Umbilicaria vellea (16.3±0.8 mg/kg; . . .59), Aspicilia calcarea (77.9±3.8 mg/kg; 88), and Cetraria islandica (22.7±1.1 mg/kg; 75) was determined as Sr. The highest CFs in lichens investigated were calculated for Sr, Ta, and Li. PLI values for Cetraria islandica, Aspicilia calcarea, and Umbilicaria vellea were greater than 1. As a result, it has been proven that these lichen species can be used as good biomonitors of pollution. Keyword: accumulation; biomonitor; lichen; pollutio More less

Direct and inverse approximation theorems of functions in the Musielak-Orlicz type spaces

Fahreddin ABDULLAYEV

Article | 2021 | Mathematical Inequalities & Applications24 ( 2 )

In Musilak-Orlicz type spaces S-M, direct and inverse approximation theorems are obtained in terms of the best approximations of functions and generalized moduli of smoothness. The question of the exact constants in Jackson-type inequalities is studied.

Best approximation-preserving operators over Hardy space

Fahreddin ABDULLAYEV

Article | 2023 | Analysis and Mathematical Physics13 ( 4 )

Let Tn be the linear Hadamard convolution operator acting over Hardy space Hq, 1≤q≤∞. We call Tn a best approximation-preserving operator (BAP operator) if Tn(en)=en, where en(z):=zn, and if ∥Tn(f)∥q≤En(f)q for all f∈Hq, where En(f)q is the best approximation by algebraic polynomials of degree a most n−1 in Hq space. We give necessary and sufficient conditions for Tn to be a BAP operator over H∞. We apply this result to establish an exact lower bound for the best approximation of bounded holomorphic functions. In particular, we show that the Landau-type inequality ∣∣fˆn∣∣+c∣∣fˆN∣∣≤En(f)∞, where c>0 and n . . . More less

О методе функционалов Ляпунова для линейного вольтеррова интегродифференциального уравнения первого порядка с запаздыванием на полуоси

Samandar İSKANDAROV

Article | 2023 | Вестник Московского университета. Серия 1: Математика. Механика ( 3 )

Устанавливаются достаточные условия, обеспечивающие оценку, ограниченность, степенную абсолютную интегрируемость на полуоси, стремление к нулю при стремлении к бесконечности независимой переменной всех решений линейного вольтеррова интегродифференциального уравнения первого порядка с запаздыванием. Для этого строится обобщенный функционал Ляпунова. Приводится иллюстративный пример. Keywords: volterra integrodifferential equation of the first order; argument lag; estimation; boundedness; absolute integrability; tending to zero of solutions; generalized method of lyapunov functionals . . . More less

Polynomial Inequalities in Quasidisks on Weighted Bergman Spaces

Fahreddin ABDULLAYEV

Article | 2017 | Ukrainian Mathematical Journal69 ( 5 )

We continue studying on the Nikol’skii and Bernstein –Walsh type estimations for complex algebraic polynomials in the bounded and unbounded quasidisks on the weighted Bergman space

Approximate Solution of the System of Linear Volterra-Stieltjes Integral Equations of the Second Kind

Avıt ASANOV | Kalıskan MATANOVA

Article | 2022 | Український математичний вісник / Ukrainian Mathematical Bulletin19 ( 1 )

A numerical solution of the system of linear Volterra-Stieltjes integral equations of the second kind has been found and analyzed using the so-called generalized trapezoid rule. Conditions for estimating the error have also been determined and justified. A solution of an example obtained using the proposed method is given. Keyword: System of linear Volterra-Stieltjes integral equations, second kind, generalized trapezoid rule, numerical solution

THE PHYSIOLOGICAL AND DNA DAMAGE RESPONSE OF IN THE LICHEN HYPOGYMNIA PHYSODES TO UV AND HEAVY METAL STRESS

Ali ASLAN

Article | 2020 | Applied Ecology and Environmental Research18 ( 2 )

This work aims to determine the response of Hypogymnia physodes (L.) Nyl. (hooded tube lichen) collected in an unpolluted site (Yenice Forest in Karabiik, Turkey) to stress conditions. In the present study, the effect of exposure to different heavy metals (Cd 2, Pb 2, and Cr 6) for different durations and UV radiations dosages on lichen was examined at the physiological and molecular levels. The effects of stress conditions were determined in the case of different parameters concerning heavy metal, protein, chlorophyll, and carotenoid contents and changes in the DNA profiles. According to the results obtained that exposure to heavy . . .metals and UV radiations leads to a physiological response in a concentration and dose-dependent manner through differences in chlorophyll, protein content in heavy metals and UV treated lichen specimen. Furthermore, changes in RAPD assay and DNA methylation analysis showed that homologous nucleotide sequences in the genome from untreated and stress conditions treated lichen specimen showed different band patterns and methylation under heavy metals and UV stress. The results determined that lichen specimen suggest as a possible bioindicator able to measure the biological effects of heavy metal pollution and damage to UV radiation More less

A Note on Dieudonne Complete Spaces

Asılbek ÇEKEEV

Article | 2018 | Filomat32 ( 14 )

In this paper, it is established a characterization of T-normal coverings by means of approximation of the Cech complete paracompacta, which are the perfect preimages of complete metric spaces of weight

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