Search results for: Banach contraction principle

Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Mohamed Houas, Maamar Benbachir

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In this paper, under weak assumptions, we study the existence and uniqueness of solutions for a nonlinear fractional boundary value problem. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using scheafer and krasnoselskii's fixed point theorem. At the end, some illustrative examples are presented.

Keywords: caputo derivative, boundary value problem, fixed point theorem, local conditions

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Authors: Abdul Hakim Khan

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The aim of the present paper is to study the Banach Space and Combinatorial Algebraic Structure of R. It is further aimed to study algebraic structure of set of all q-extension of classical formula and function for 0 < q < 1.

Keywords: integral functions, q-extensions, q numbers of metric space, algebraic structure of r and banach space

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Authors: Irina Peterburgsky

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Let T be a unit circumference of a complex plane, E be a Banach space, E* and E** be its conjugate and second conjugate, respectively. In general, a Hardy space Hp(E), p ≥1, where functions act from the open unit disk to E, could contain a function for which even weak nontangential (angular) boundary value in the space E** does not exist at any point of the unit circumference T (C. Grossetete.) The situation is "better" when certain restrictions to the Banach space of values are applied (more or less resembling a classical case of scalar-valued functions depending on constrains, as shown by R. Ryan.) This paper shows that, nevertheless, in the case of a Banach space of a general type, the following positive statement is true: Proposition. For any function f(z) from Hp(E), p ≥ 1, there exists a function F(eiθ) on the unit circumference T to E** whose Poisson (in the Pettis sense) is integral regains the function f(z) on the open unit disk. Some characteristics of the function F(eiθ) are demonstrated.

Keywords: hardy spaces, Banach space-valued function, boundary values, Pettis integral

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Authors: Awais Asif

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This article investigates fixed point theorems of Chatterjea type F-contraction in the setting of F-metric space. We relax the conditions of F-contraction and define modified F-contraction for two mappings. The study provides fixed point results for both single-valued and multivalued mappings. The results are further extended to common fixed point theorems for two mappings. Moreover, to discuss the applicability of our results, an application is provided, which shows the role of our results in finding the solution to functional equations in dynamic programming. Our results generalize and extend the existing results in the literature.

Keywords: Chatterjea type F-contraction, F-cauchy sequence, F-convergent, multi valued mappings

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Authors: Hemant Kumar Pathak

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In 1994, Matthews (S.G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197) introduced the concept of a partial metric as a part of the study of denotational semantics of data flow networks. He gave a modified version of the Banach contraction principle, more suitable in this context. In fact, (complete) partial metric spaces constitute a suitable framework to model several distinguished examples of the theory of computation and also to model metric spaces via domain theory. In this paper, we introduce the concept of almost partial Hausdorff metric. We prove a fixed point theorem for multi-valued mappings on partial metric space using the concept of almost partial Hausdorff metric and prove an analogous to the well-known Nadler’s fixed point theorem. In the sequel, we derive a homotopy result as an application of our main result.

Keywords: fixed point, partial metric space, homotopy, physical sciences

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Authors: Bayan Almofty, Yuto Yamaki, Tadamasa Terai, Sadahito Uto

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Culture techniques of skeletal muscle cells are advanced in the field of regenerative medicine and applied research of cultured muscle. As applied research of cultured muscle, myopathy (muscles disease) treatment is expected and development bio of actuator is also expected in biomedical engineering. Grayanotoxins (GTXs) is known as neurotoxins that enhance the permeability of cell membrane for Na ions. Grayanotoxins are extracted from a famous Pieris japonica and Ericaceae as well as a phytotoxin. In this study, we investigated the effect of GTXs on muscle cells (C2C12) contraction and membrane potential. Contraction of myotubes is induced by applied external electrical stimulation. Contraction and membrane potential change of skeletal muscle cells are induced by injection of current. We, therefore, concluded that effect of Grayanotoxins on contraction and membrane potential of C2C12 relate to acute toxicity of GTXs.

Keywords: skeletal muscle cells C2C12, grayanotoxins, contraction, membrane potential, acute toxicity, pytotoxin, motubes

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Authors: Muslim Malik, Avadhesh Kumar

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A stronger concept of exact controllability which is called Total Controllability is introduced in this manuscript. Sufficient conditions have been established for the total controllability of a control problem, governed by second order nonlinear differential equation with delay and non-instantaneous impulses in a Banach space X. The results are obtained using the strongly continuous cosine family and Banach fixed point theorem. Also, the total controllability of an integrodifferential problem is investigated. At the end, some numerical examples are provided to illustrate the analytical findings.

Keywords: Banach fixed point theorem, non-instantaneous impulses, strongly continuous cosine family, total controllability

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Authors: Pejman Taghibeikzadehbadr

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Muscle contraction stimulates a transient change of myogenic factors, partly related to the mode of contractions. Here, we assessed the response of Insulin-like growth factor 1Ea (IGF-1Ea), Insulin-like growth factor 1Eb (IGF-1Eb), Insulin-like growth factor 1Ec (IGF-1Ec), Peroxisome proliferator-activated receptor gamma coactivator 1-alpha (PGC1α-1), Peroxisome proliferator-activated receptor gamma coactivator 4-alpha (PGC1α-4), and myostatin to the eccentric Vs the concentric contraction in human skeletal muscle. Ten healthy males were performed an acute eccentric and concentric exercise bout (n = 5 per group). For each contraction type, participants performed 12 sets of 10 repetitions knee extension by the dominant leg. Baseline and post-exercise muscle biopsy were taken 4 weeks before and immediately after experimental sessions from Vastus Lateralis muscle. Genes expression was measured by real-time PCR technique. There was a significant increase in PGC1α-1, PGC1α-4, IGF-1Ea and, IGF-1Eb mRNA after concentric contraction (p ≤ 0.05), while the PGC1α-4 and IGF-1Ec significantly increased after eccentric contraction (p ≤ 0.05). It is intriguing to highlight that; no significant differences between groups were evident for changes in any variables following exercise bouts (p ≥ 0.05). Our results found that concentric and eccentric contractions presented different responses in PGC1α-1, IGF-1Ea, IGF-1Eb, and IGF-1Ec mRNA. However, a similar significant increase in mRNA content was observed in PGC1α-4. Further, no apparent differences could be found between the response of genes to eccentric and concentric contraction.

Keywords: eccentric contraction, concentric contraction, gene expression, PGC-1 alpha, IGF-1 Myostatin

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Authors: Manal Azzidani

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This research consideres the extension of special functions called Positive Linear Operators. the bounded linear operator which defined from normed space to Banach space will extend to the closure of the its domain, And extend identified linear functional on a vector subspace by Hana-Banach theorem which could be generalized to the positive linear operators.

Keywords: extension, positive operator, Riesz space, sublinear function

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Authors: Bayan Almofty, Yuto Yamaki, Tadamasa Terai, Sadahito Uto

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Myopathy (muscles disease) treatment are expected in the field of regenerative medicine and applied research of cultured muscle to bio actuator is performed in Biomedical Engineering as applied research of cultured muscle. This study is about cultured myoblast C2C12 from mouse skeletal muscle and a mechanism of cultured muscle contraction by electric stimulation is investigated. Grayanotoxins (GTXs) belong to neurotoxins known to enhance the permeability of cell membrane for Na ions. Grayanotoxins are extracted from a famous Pieris japonica and Ericaceae as a phytotoxin. We investigated the functional role of GTXs on muscle cells (C2C12) contraction and membrane potential. A change in membrane potential is measured using a micro glass tube electrode contraction of myotubes is induced by applying an external electrical stimulation. The contraction and membrane potential change induced by injection of current using the micro glass electrode are also measured. From the result, contraction and membrane potential of muscle cells was affected by GTXs treatment, suggesting that the diverse chemical structures of GTXs are responsible for contraction and membrane potential of muscle cells.

Keywords: skeletal muscle, C2C12, myoblast, myotubes, contraction, Grayanotoxins, membrane potential, neurotoxins, phytotoxin

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Authors: Felix Damilola Ajibade, Opeyemi O. Enoch, Taiwo Paul Fajusigbe

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This paper is centered on conducting an inquiry into the stability of the F* iterative algorithm to the fixed point of a strongly pseudo-contractive mapping in the framework of uniformly convex Banach spaces. To achieve the desired result, certain existing inequalities in convex Banach spaces were utilized, as well as the stability criteria of Harder and Hicks. Other necessary conditions for the stability of the F* algorithm on strong pseudo-contractive mapping were also obtained. Through a numerical approach, we prove that the F* iterative algorithm is H-stable for strongly pseudo-contractive mapping. Finally, the solution of the mixed-type Volterra-Fredholm functional non-linear integral equation is estimated using our results.

Keywords: stability, F* -iterative algorithm, pseudo-contractive mappings, uniformly convex Banach space, mixed-type Volterra-Fredholm integral equation

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Authors: Hichem Ramoul

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In this work, we introduce a new type of contractive maps and we establish a new fixed point theorem for the class of almost θ-contractions (more general than the class of almost contractions) in a complete generalized metric space. The major novelty of our work is to prove a new fixed point result by weakening some hypotheses imposed on the function θ which will change completely the classical technique used in the literature review to prove fixed point theorems for almost θ-contractions in a complete generalized metric space.

Keywords: almost contraction, almost θ-contraction, fixed point, generalized metric space

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Authors: M. H. M. Rashid

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A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.

Keywords: Weyl's Theorem, Weyl Spectrum, Polaroid operators, property (gm)

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Authors: Alexey Yu. Martynov, Sulejman Bayramov

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Introduction: The myocardial bridging is the most common anomaly of the coronary arteries (CA). Depending on the examination method, the frequency of detected myocardial bridges (MB) varies in a rather wide range. The typical clinical manifestations of MB are angina pectoris, arrhythmias, sudden cardiac death. Objective: To study the incidence of MB in patients hospitalized with coronary artery disease (CAD). To assess clinical manifestations of MB in patients admitted with CAD. Materials and methods: A retrospective analysis of 19159 case histories of patients admitted at clinical city hospital in Moscow from 01.01.2018 to 31.12 2019 with CAD was performed. 9384 patients’ coronary angiographies (CAG) were examined for MB. The localization of MB, the degree of coronary contraction by MB, the number of MB, isolated MB and combined with CAD were assessed. The clinical manifestations of MB were determined. Results: MB was detected in 52 patients all with one myocardial bridge. 20 patients with MB have intact CA, and 32 patients have MB combined with CAD. Among 20 patients with intact CA: I degree of MB contraction (up to 50%) was detected in 9 patients. Clinical manifestations in five cases were angina pectoris, in 3 myocardial infarction (MI) - 1 patients with ST segment elevation MI (STEMI), 2 without ST segment elevation MI (NSTEMI), 1 post-infarction cardiosclerosis (PICS). Stable angina II FC in 3, III FC in 1, vasospastic angina (VSA) in 1 patient. II degree of MB contraction (up to 50-70%) was determined in 9 patients: in seven cases angina pectoris was detected, 1 NSTEMI, 1 PICS. Stable angina II FC in 3, III FC in 1, VSA in 3 patients. III degree of MB contraction (> 70%) detected in 2 patients. II FC stable angina in one case, PICS in another. Among 32 patients having MB combined with CAD I degree of MB contraction was observed in 20 patients. Clinical manifestations in 12 cases were angina pectoris in 8 II FC and in 4 III FC, 7 MI 6 with STEMI and 1 NSTEMI, 1 PICS. II degree of MB contraction was detected in 7 patients, 4 of them had angina pectoris, 3 MI 2 with STEMI and 1 NSTEMI. Stable angina II FC in 3, VSA in 1 patients. III degree of MB contraction was diagnosed in five patients. In two cases, II FC and III FC stable angina were observed, 2 MI with STEMI and NSTEMI, 1 PICS. Conclusions: MB incidence is one in 368 patients with CAD. The most common involvement (68%) is MB combined with CA atherosclerotic lesions. MB with intact CA are detected in one-third (32%) of patients. The first-degree MB contraction is most frequent condition. MI is more often detected in intact CA with first degree MB than in the second degree. The degree of MB contraction was not correlated with the severity of the clinical manifestations.

Keywords: clinical manifestations, coronary angiography, coronary artery disease, myocardial bridging, myocardial infarction, stable angina

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Authors: Alemayehu Geremew Geremew

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We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E.

Keywords: common fixed point, Mann iteration, multivalued mapping, weak convergence

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Authors: Mohamed M. Ragab, Neveen A. Abdel Raoof, Reham H. Diab

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Background: Delayed onset muscle soreness (DOMS) is the most common symptom when ordinary individuals and athletes are exposed to unaccustomed physical activity, especially eccentric contraction which impairs athletic performance, ordinary people work ability and physical functioning. A multitude of methods have been investigated to reduce DOMS. One of the valuable method to control DOMS is repeated bout effect (RBE) as a prophylactic method. Purpose: To compare the repeated bout effect of submaximal eccentric contraction versus maximal isometric contraction on induced DOMS. Methods: Sixty normal male volunteers were assigned randomly into three groups of equal number: Group (A) “first study group”: 20 subjects received submaximal eccentric contraction on non-dominant elbow flexors as prophylactic exercise. Group (B) “second study group”: 20 subjects received maximal isometric contraction on non-dominant elbow flexors as prophylactic exercise. Group (C) “control group”: 20 subjects did not receive any prophylactic exercise. Maximal isometric contraction peak torque of elbow flexors and patient related elbow evaluation (PREE) scale were measured for each subject 3 times before, immediately after and 48 hours after induction of DOMS. Results: Post-hoc test for maximal isometric peak torque and PREE scale immediately and 48 hours after induction of DOMS revealed that group (A) and group (B) resulted in significant decrease in maximal isometric strength loss and elbow pain and disability rather than control group (C), but submaximal eccentric group (A) was more effective than maximal isometric group (B) as it showed more rapid recovery of functional strength and less degrees of elbow pain and disability. Conclusion: Both submaximal eccentric contraction and maximal isometric contraction were effective in prevention of DOMS but submaximal eccentric contraction had the greatest protective effect.

Keywords: delayed onset muscle soreness, maximal isometric peak torque, patient related elbow evaluation scale, repeated bout effect

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Authors: Umar Yusuf Batsari

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Let E be a uniformly smooth and uniformly convex real Banach space and C be a nonempty, closed and convex subset of E. Let $V= \{S_i : C\to C, ~i=1, 2, 3\cdots N\}$ be a convex set of relatively nonexpansive mappings containing identity. In this paper, an iterative sequence obtained from CQ algorithm was shown to have strongly converge to a point $\hat{x}$ which is a common fixed point of relatively nonexpansive mappings in V and also solve the system of equilibrium problems in E. The result improve some existing results in the literature.

Keywords: relatively nonexpansive mappings, strong convergence, equilibrium problems, uniformly smooth space, uniformly convex space, convex set, kadec klee property

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Authors: Entfellner Manuel, Wannenmacher Helmut, Reisenbauer Josef, Schubert Wulf

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When tunnelling in overstressed weak rocks ("squeezing ground"), two basic design approaches are available: the resistance principle, and the yielding principle. The resistance principle relies on rigid support systems to withstand the ground pressure. Alternatively, the yielding principle prioritizes controlled deformation, allowing the ground to deform without compromising tunnel integrity. This paper highlights the beneficial factors of the yielding principle for conventionally excavated tunnels in overstressed weak rocks. Especially the application of a ductile shotcrete lining with yielding elements is analysed in detail. Construction costs, safety, short- and long-term stabilities are discussed.

Keywords: squeezing ground, yielding principle, yielding element, conventional tunneling

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Authors: Xincheng He, Weijun Gao, Gangwei Cai

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In the process of rapid urbanization, large-scale industrial production, and unreasonable planning and construction have caused various ecological and environmental problems, while hindered the sustainable development of cities. The ecological district not only realizes the coordinated development of society, economy, and environment but also conforms to the trend of smart contraction of the development of cities in China from the periphery to the center. This paper reviews the development of China's ecological district, including the full life cycle process of policy, planning, implementation, and operation. Based on sorting out the concept, connotation, and development status of China’s ecological district, the relationship between the construction of the ecological district and the sustainable city is discussed. Summarizing the development trend of the ecological district, the ecological district should combine the construction of smart cities, actively respond to the digital information era, and improve the construction of the ecological district system. It proposes that the future direction of city's sustainable development needs to change from a thematic focus on ecology to the common urbanization of humanity, society, and nature. Focusing on people-oriented, ecological, and digital future communities will become an important construction method for the city's sustainable smart contraction.

Keywords: eco-district, smart contraction, sustainable development, future community

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Authors: CM van der Bank, Marjoné van der Bank

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International and domestic environmental law has evolved quite rapidly in the last few decades. At the international level the Stockholm and Rio Declarations paved the way for a broad based consensus of the international community on environmental issues and principles. At the Domestic level also many states have incorporated environmental protection in their constitutions and even more states are doing the same at least in their domestic legislations. In this process of evolution environmental law has unleashed a number of novel principles such as; the participatory principle, the polluter pays principle, the precautionary principle, the inter-generational and intra-generational principles, the prevention principle, the sustainable development principle and so on.

Keywords: environment, human rights, international law, protection

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Authors: Roslina Che Soh

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Best interest of the child has been the prevailing principle of the custody legislations of most nations in the world. The tremendous shift from parental rights to parental responsibilities throughout the centuries had made the principle of best interests of the child as the utmost matter which parents must uphold in child upbringing. Despite the commitment to this principle is significantly enshrined in the United Nation Convention on Rights of the Child, the content and application of the principle differs across borders. Differences persist notwithstanding many countries have experienced a substantial shift over the last several decades in the types of custodial arrangements that are thought to best serve children’s interests. The laws in Malaysia similarly uphold this principle but do not provide further deliberation on the principle itself. The principle is entirely developed by the courts through decided cases. Thus, this paper seeks to discuss the extent of the application of best interest of the child principle in custody disputes. In doing so, it attempts to provide an overview of the current laws and the approach of the Civil and the Shariah courts in Malaysia in applying the principle in determining custody disputes. For purposes of comparison, it briefly examines the legislations and the courts practices in Australia and England on this matter. The purpose is to determine the best standard to be adopted by Malaysia and to propose improvement to the laws whenever appropriate.

Keywords: child custody, best interest, Malaysian law, bioinformatics, biomedicine

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Authors: Subrat Partha Sarathi Pattnaik, Rajan N.K.S.

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Integrated rocket ramjet engines are highly suitable for long range missile applications. Designing the fixed geometry intakes for such missiles that can operate efficiently over a range of operating conditions is a highly challenging task. Hence, the present study aims to evaluate the effect of throat design on the performance of a rectangular mixed compression intake for operation in the Mach number range of 1.8 – 2.5. The analysis has been carried out at four different Mach numbers of 1.8, 2, 2.2, 2.5 and two angle-of-attacks of +5 and +10 degrees. For the throat design, three different throat heights have been considered, one corresponding to a 3- external shock design and two heights corresponding to a 2-external shock design leading to different internal contraction ratios. The on-design Mach number for the study is M 2.2. To obtain the viscous flow field in the intake, the theoretical designs have been considered for computational fluid dynamic analysis. For which Favre averaged Navier- Stokes (FANS) equations with two equation SST k-w model have been solved. The analysis shows that for zero angle of attack at on-design and high off-design Mach number operations the three-ramp design leads to a higher total pressure recovery (TPR) compared to the two-ramp design at both contraction ratios maintaining same mass flow ratio (MFR). But at low off-design Mach numbers the total pressure shows an opposite trend that is maximum for the two-ramp low contraction ratio design due to lower shock loss across the external shocks similarly the MFR is higher for low contraction ratio design as the external ramp shocks move closer to the cowl. At both the angle of attack conditions and complete range of Mach numbers the total pressure recovery and mass flow ratios are highest for two ramp low contraction design due to lower stagnation pressure loss across the detached bow shock formed at the ramp and lower mass spillage. Hence, low contraction design is found to be suitable for higher off-design performance.

Keywords: internal contraction ratio, mass flow ratio, mixed compression intake, performance, supersonic flows

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Authors: Emmanuel Kamal Aziz Saba, Gihan Abd El-Lateif Younis El-Tantawi, Mohammed Hamdy Zahran, Ibrahim Khalil Ibrahim, Mohammed Abd El-Salam Shehata, Hussein Al-Moghazy Sultan, Medhat Mohamed Anwar

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Examination of the external anal sphincter muscle strength of voluntary contraction is essential in initial assessment and assessment of efficacy of rehabilitation of patients with faecal incontinence (FI) and obstructed defecation (OD). The present study was conducted to evaluate the digital assessment of the external anal sphincter muscle strength of voluntary contraction by using Modified Oxford Scale (MOS) in comparison to anal manometry squeeze pressure. The present cross-sectional study included 65 patients. There were 40 patients (61.5 %) with FI and 25 patients (38.5 %) with OD. All patients were subjected to history taking, clinical examination including assessment of the external anal sphincter muscle strength of voluntary contraction by using MOS and anal manometry (mean squeeze pressure and maximal squeeze pressure). There was a statistically significant positive correlation between MOS and anal manometry squeeze pressures including mean squeeze pressure and maximal squeeze pressure among FI group and OD group. In conclusion, assessment of the external anal sphincter muscle strength of voluntary contraction by using MOS is a valid method and can substitute anal manometry assessment.

Keywords: anal manometry, external anal sphincter muscle, Modified Oxford Scale, muscle strength

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Authors: M. Otrusinova, E. Pastuszkova

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The article is addressing the currently ongoing reform processes of transforming the public finance accounting based on cash flow principle to accrual principle. The presented analysis concerns the issues associated with the introduction of the state accounting from the perspective of municipal employees in compiling the opinions of financial experts in conditions of the Czech Republic. The aim of this paper is to present outcomes of analysis focused on currently discussed topics which are related to introducing the accrual principle into accounting of selected entities, especially municipalities and municipality-funded institutions. The output of the paper consists of comparing the application of the accrual principle in the financial reporting of municipalities in the Czech Republic and Slovakia. In conclusion and based on the survey, respondents from Slovak municipalities that have already adopted the accrual accounting principle show better opinion than Czech municipalities.

Keywords: accrual principle, accounting, accounting reform, Czech Republic, municipalities, public finance

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Authors: Sahib Dino Naseerani

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The presented scientific text discusses the concept of imaginary pressure and its role in different relative motions. It explores how imaginary pressure, which is the combined effect of external atmospheric pressure and real pressure, affects various substances and their physical properties. The study aims to understand the impact of imaginary pressure and its potential applications in different contexts, such as spaceflight. The main objective of this study is to investigate the role of imaginary pressure on different relative motions. Specifically, the researchers aim to examine how imaginary pressure affects the contraction and mass variation of a body when it is in motion at the speed of light. The study seeks to provide insights into the behavior and consequences of imaginary pressure in various scenarios. The data was collected using three research papers. This research contributes to a better understanding of the theoretical implications of imaginary pressure. It elucidates how imaginary pressure is responsible for the contraction and mass variation of a body in motion, particularly at the speed of light. The findings shed light on the behavior of substances under the influence of imaginary pressure, providing valuable insights for future scientific studies. The study addresses the question of how imaginary pressure influences various relative motions and their associated physical properties. It aims to understand the role of imaginary pressure in the contraction and mass variation of a body, particularly at high speeds. By examining different substances in liquid and solid forms, the research explores the consequences of imaginary pressure on their volume, length, and mass.

Keywords: imaginary pressure, contraction, variation, relative motion

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Authors: Hudson Akewe

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This research presents complementary results with wider applications on convergence and rate of convergence of classical fixed point theory in Banach spaces to the world of the theory of fixed points of mappings defined in classes of spaces of measurable functions, known in the literature as modular function spaces. The study gives a comprehensive survey of various iterative fixed point results for the classes of multivalued ρ-contractive-like, ρ-quasi-contractive-like, ρ-quasi-contractive, ρ-Zamfirescu and ρ-contraction mappings in the framework of modular function spaces. An example is presented to demonstrate the applicability of the implicit-type iterative schemes to the system of ordinary differential equations. Furthermore, numerical examples are given to show the rate of convergence of the various explicit Kirk-type and implicit Kirk-type iterative schemes under consideration. Our results complement the results obtained on normed and metric spaces in the literature. Also, our methods of proof serve as a guide to obtain several similar improved results for nonexpansive, pseudo-contractive, and accretive type mappings.

Keywords: implicit Kirk-type iterative schemes, multivalued mappings, convergence results, fixed point

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Authors: Ginger Egberts, Fred Vermolen, Paul van Zuijlen

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One of the common complications in post-burn scars is contractions. Depending on the extent of contraction and the wound dimensions, the contracture can cause a limited range-of-motion of joints. A one-dimensional morphoelastic continuum hypothesis-based model describing post-burn scar contractions is considered. The beauty of the one-dimensional model is the speed; hence it quickly yields new results and, therefore, insight. This model describes the movement of the skin and the development of the strain present. Besides these mechanical components, the model also contains chemical components that play a major role in the wound healing process. These components are fibroblasts, myofibroblasts, the so-called signaling molecules, and collagen. The dermal layer is modeled as an isotropic morphoelastic solid, and pulling forces are generated by myofibroblasts. The solution to the model equations is approximated by the finite-element method using linear basis functions. One of the major challenges in biomechanical modeling is the estimation of parameter values. Therefore, this study provides a comprehensive description of skin mechanical parameter values and a sensitivity analysis. Further, since skin mechanical properties change with aging, it is important that the model is feasible for predicting the development of contraction in burn patients of different ages, and hence this study provides a feasibility study. The variability in the solutions is caused by varying the values for some parameters simultaneously over the domain of computation, for which the results of the sensitivity analysis are used. The sensitivity analysis shows that the most sensitive parameters are the equilibrium concentration of collagen, the apoptosis rate of fibroblasts and myofibroblasts, and the secretion rate of signaling molecules. This suggests that most of the variability in the evolution of contraction in burns in patients of different ages might be caused mostly by the decreasing equilibrium of collagen concentration. As expected, the feasibility study shows this model can be used to show distinct extents of contractions in burns in patients of different ages. Nevertheless, contraction formation in children differs from contraction formation in adults because of the growth. This factor has not been incorporated in the model yet, and therefore the feasibility results for children differ from what is seen in the clinic.

Keywords: biomechanics, burns, feasibility, fibroblasts, morphoelasticity, sensitivity analysis, skin mechanics, wound contraction

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Authors: Smita Shenoy, Amoolya Gowda, Tara Shanbhag, Krishnananda Prabhu, Venumadhav Nelluri

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The study was undertaken to assess the effect of ethanolic extract of Michelia champaca on excision wound healing in diabetic wistar rats. Excision wound was made in five groups of rats after inducing diabetes with streptozotocin in four groups. Paraffin was applied to wounds in nondiabetic and diabetic control and 2.5%, 5%, 10% ointment of extract to wounds in three diabetic test groups. Monitoring of wound contraction rate, the period of epithelization and histopathological examination of granulation tissue was done. There was a significant (p < 0.05) decrease in the period of epithelization and a significant increase in the wound contraction rate on day 12 and 16 in rats treated with 5% and 10% ointment as compared to diabetic rats. There was a better organization of collagen fibers in the granulation tissue of wounds treated with 10% ointment. The higher dose of ethanolic extract of Michelia champaca promoted wound healing in diabetic Wistar rats.

Keywords: Michelia champaca, excision wound, contraction, epithelization

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Authors: Swati Kundu, Seemi Farhat Basir, Luqman A. Khan

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Acute and chronic exposure to arsenic and mercury is known to produce vasoconstriction. Pathways involved in this hypercontraction and their relative contribution are not understood. In this study, we measure agonist-induced contraction of isolated rat aorta exposed to arsenic and mercury aorta and delineate pathways mediating this effect. PE-induced hypercontraction of 37% and 32% was obtained with 25 µM As(III) and 6 nM Hg(II), respectively. Isometric contraction measurements in the presence of apocynin, verapamil and sodium nitroprusside indicates that the major cause of increased contraction is reactive oxygen species and depletion of nitric oxide. Calcium influx plays a minor role in both arsenic and mercury caused hypercontraction. In the unexposed aorta, eugenol causes relaxation by inhibiting ROS and elevating NO, linalool by blocking voltage dependent calcium channel (VDCC) and elevating NO, and carvone by blocking calcium influx through VDDC. Since arsenic and mercury caused hypercontraction is mediated by increased ROS and depletion of nitric oxide, we hypothesize that molecules which neutralize ROS or elevate NO will be better ameliorators. In line with this argument, we find eugenol to be the best ameliorator of arsenic and mercury hypercontraction followed by linalool and carvone.

Keywords: carvone, eugenol, linalool, mercury

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