Search results for: Dirichlet eta lambda beta functions

Authors: Slobodan B. Tričković

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We present the results concerned with trigonometric series that include sine and cosine functions with a parameter appearing in the denominator. We derive two types of closed-form formulas for trigonometric series. At first, for some integer values, as we know that Riemann’s ζ function and Dirichlet η, λ equal zero at negative even integers, whereas Dirichlet’s β function equals zero at negative odd integers, after a certain number of members, the rest of the series vanishes. Thus, a trigonometric series becomes a polynomial with coefficients involving Riemann’s ζ function and Dirichlet η, λ, β functions. On the other hand, in some cases, one cannot immediately replace the parameter with any positive integer because we shall encounter singularities. So it is necessary to take a limit, so in the process, we apply L’Hospital’s rule and, after a series of rearrangements, we bring a trigonometric series to a form suitable for the application of Choi-Srivastava’s theorem dealing with Hurwitz’s zeta function and Harmonic numbers. In this way, we express a trigonometric series as a polynomial over Hurwitz’s zeta function derivative.

Keywords: Dirichlet eta lambda beta functions, Riemann's zeta function, Hurwitz zeta function, Harmonic numbers

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Authors: Muhammad Sufian Jusoh, Mesliza Mohamed

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In this paper, we investigate the existence of positive solutions for a Dirichlet second order boundary value problem by applying the Krasnosel'skii fixed point theorem on compression and expansion of cones.

Keywords: Krasnosel'skii fixed point theorem, positive solutions, Dirichlet boundary value problem, Dirichlet second order boundary problem

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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Authors: F. Berna Benli, Özgür Keskin

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Lately, many mathematicians have been studied the statistical convergence of a sequence of fuzzy numbers. We know that Lambda-statistically convergence is a kind of convergence between ordinary convergence and statistical convergence. In this paper, we will introduce the new kind of convergence such as λ-levelwise statistical convergence. Then, we will define the concept of the λ-levelwise statistical cluster and limit points of a sequence of fuzzy numbers. Also, we will discuss the relations between the sets of λ-levelwise statistical cluster points and λ-levelwise statistical limit points of sequences of fuzzy numbers. This work has been extended in this paper, where some relations have been considered such that when lambda-statistical limit inferior and lambda-statistical limit superior for lambda-statistically convergent sequences of fuzzy numbers are equal. Furthermore, lambda-statistical boundedness condition for different sequences of fuzzy numbers has been studied.

Keywords: fuzzy number, λ-levelwise statistical cluster points, λ-levelwise statistical convergence, λ-levelwise statistical limit points, λ-statistical cluster points, λ-statistical convergence, λ-statistical limit points

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Authors: Khaled Moaddy

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In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

Keywords: standard finite difference schemes, non-standard schemes, Laplace equation, Dirichlet boundary conditions

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Authors: Lawrence A. Farinola

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Four point implicit schemes for the approximation of the first and pure second order derivatives for the solution of the Dirichlet problem for one dimensional Schrodinger equation with respect to the time variable t were constructed. Also, special four-point implicit difference boundary value problems are proposed for the first and pure second derivatives of the solution with respect to the spatial variable x. The Grid method is also applied to the mixed second derivative of the solution of the Linear Schrodinger time-dependent equation. It is assumed that the initial function belongs to the Holder space C⁸⁺ᵃ, 0 < α < 1, the Schrodinger wave function given in the Schrodinger equation is from the Holder space Cₓ,ₜ⁶⁺ᵃ, ³⁺ᵃ/², the boundary functions are from C⁴⁺ᵃ, and between the initial and the boundary functions the conjugation conditions of orders q = 0,1,2,3,4 are satisfied. It is proven that the solution of the proposed difference schemes converges uniformly on the grids of the order O(h²+ k) where h is the step size in x and k is the step size in time. Numerical experiments are illustrated to support the analysis made.

Keywords: approximation of derivatives, finite difference method, Schrödinger equation, uniform error

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Authors: Hsien Hao Teng

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This study uses numerical simulation to analyze the aerodynamic characteristics of the 53-degree Lambda wing with a sweep angle and mainly discusses the numerical simulation results and physical characteristics of the wall y+. Use the commercial software Fluent to execute Mach number 0.15; when the angle of attack attitude is between 0 degrees and 27 degrees, the physical characteristics of the overall aerodynamic force are analyzed, especially when the fluid separation and vortex structure changes are discussed under the condition of high angle of attack, it will affect The instability of pitching moment. In the numerical calculation, the use of wall y+ and turbulence model will affect the prediction of vortex generation and the difference in structure. The analysis results are compared with experimental data to discuss the trend of the aerodynamic characteristics of the Lambda wing.

Keywords: lambda wing, wall function, turbulence model, computational fluid dynamics

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Authors: I. Grigoraviciute-Puroniene, K. Tsuru, E. Garskaite, Z. Stankeviciute, A. Beganskiene, K. Ishikawa, A. Kareiva

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Tricalcium phosphate (β-Ca₃(PO₄)₂, β-TCP) powders were synthesized using wet polymeric precipitation method for the first time to our best knowledge. The results of X-ray diffraction analysis showed the formation of almost single a Ca-deficient hydroxyapatite (CDHA) phase of a poor crystallinity already at room temperature. With continuously increasing the calcination temperature up to 800 °C, the crystalline β-TCP was obtained as the main phase. It was demonstrated that infrared spectroscopy is very effective method to characterize the formation of β-TCP. The SEM results showed that β-TCP solids were homogeneous having a small particle size distribution. The β-TCP powders consisted of spherical particles varying in size from 100 to 300 nm. Fabricated β-TCP specimens were placed to the bones of the rats and maintained for 1-2 months.

Keywords: Tricalcium phosphate (β-Ca3(PO4)2, bone regeneration, wet chemical processing, polymeric precipitation

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Authors: Vinod Nair, C. Sadasivan

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Beta-lactam antibiotics are the most frequently prescribed medications in modern medicine. The antibiotic resistance by the production of enzyme beta-lactamase is an important mechanism seen in microorganisms. Resistance to beta-lactams mediated by beta-lactamases can be overcome successfully with the use of beta-lactamase inhibitors. New generations of the antibiotics contain mostly synthetic compounds, and many side effects have been reported for them. Combinations of beta-lactam and beta-lactamase inhibitors have become one of the most successful antimicrobial strategies in the current scenario of bacterial infections. Plant-based drugs are very cheap and having lesser adverse effect than synthetic compounds. The synergistic effect of eugenol acetate with beta-lactams restores the activity of beta-lactams, allowing their continued clinical use. It is reported here the enhanced inhibitory effect of phytochemical, eugenol acetate, isolated from the plant Syzygium aromaticum with beta-lactams on beta-lactamase. The compound was found to have synergistic effect with the antibiotic amoxicillin against antibiotic-resistant strain of S.aureus. The enzyme was purified from the organism and incubated with the compound. The assay showed that the compound could inhibit the enzymatic activity of beta-lactamase. Modeling and molecular docking studies indicated that the compound can fit into the active site of beta-lactamase and can mask the important residue for hydrolysis of beta-lactams. The synergistic effects of eugenol acetate with beta-lactam antibiotics may justify, the use of these plant compounds for the preparation of β-lactamase inhibitors against β-lactam resistant S.aureus.

Keywords: betalactamase, eugenol acetate, synergistic effect, molecular modeling

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Authors: Naoual Boussoualim, Hayat Trabsa, Iman Krache, Lekhmici Arrar, Abderrahmane Baghiani

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Resistance to antibiotics has emerged following their widespread use; the important mechanism of beta-lactam resistance in bacteria is the production of beta-lactamase. In order to find new bioactive beta-lactamase inhibitors, this study investigated the inhibition effect of the extracts of Anchusa azurea (AA) on a beta-lactamase from Bacillus cereus. The extracts exerted inhibitory effects on beta-lactamase in a dose-dependent manner, the results showed that the crude extract (BrE) and the ethyl acetate extract (AcE) of Anchusa azurea showed a very high inhibitory activity at a concentration of 10 mg, the percentage of inhibition was between 58% and 68%. Not all extracts were as potent as the original inhibitors such as clavulanic acid, the isolation and the structural elucidation of the active constituents in these extracts will provide useful means in the development of beta -lactamase inhibitors.

Keywords: Anchusa azurea, natural product, resistance, antibiotics, beta-lactamase, inhibitors

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Authors: Wei Tian, Jie Liang, Hammad Naveed

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Beta-barrel membrane proteins are found in the outer membrane of gram-negative bacteria, mitochondria, and chloroplasts. They carry out diverse biological functions, including pore formation, membrane anchoring, enzyme activity, and bacterial virulence. In addition, beta-barrel membrane proteins increasingly serve as scaffolds for bacterial surface display and nanopore-based DNA sequencing. Due to difficulties in experimental structure determination, they are sparsely represented in the protein structure databank and computational methods can help to understand their biophysical principles. We have developed a novel computational method to predict the 3D structure of beta-barrel membrane proteins using evolutionary coupling (EC) constraints and a reduced state space. Combined with an empirical potential function, we can successfully predict strand register at > 80% accuracy for a set of 49 non-homologous proteins with known structures. This is a significant improvement from previous results using EC alone (44%) and using empirical potential function alone (73%). Our method is general and can be applied to genome-wide structural prediction.

Keywords: beta-barrel membrane proteins, structure prediction, evolutionary constraints, reduced state space

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Authors: A. Calvin Antony, Sakthi Kumar Arul Prakash, V. R. Sanal Kumar

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In this paper a unique alpha-beta double piston 'stirling engine' is designed, manufactured and conducted laboratory test to ameliorate the efficiency of the stirling engine. The paper focuses on alpha and beta type engines, capturing their benefits and eradicating their short comings; along with the output observed from the flywheel. In this model alpha engine is kinematically with a piston cylinder arrangement which works quite like a beta engine. The piston of the new cylinder is so designed that it replicates a glued displacer and power piston as similar to that of beta engine. The bigger part of the piston is the power piston, which has a gap around it, while the smaller part of the piston is tightly fit in the cylinder and acts like the displacer piston. We observed that the alpha-beta double piston stirling engine produces 25% increase in power compare to a conventional alpha stirling engine. This working model is a pointer towards for the design and development of an alpha-beta double piston Stirling engine for industrial applications for producing electricity from the heat producing exhaust gases.

Keywords: alpha-beta double piston stirling engine , alpha stirling engine , beta double piston stirling engine , electricity from stirling engine

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Authors: Bharti Chogtu Magazine, Dhanya Soodana Mohan, Shruti Nair, Tanwi Trushna

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The study was undertaken to analyse the cardiovascular drugs being prescribed in patients with concomitant reactive airway disease and hypertension or ischemic heart diseases (IHD). Also, the effect of beta-blockers on respiratory symptoms in these patients was recorded. Data was collected from medical records of patients with reactive airway disease and concomitant hypertension and IHD. It included demographic details of the patients, diagnosis, drugs prescribed and the patient outcome regarding the exacerbation of asthma symptoms with intake of beta blockers. Medical records of 250 patients were analysed.13% of patients were prescribed beta-blockers. 12% of hypertensive patients, 16.6% of IHD patients and 20% of patients with concomitant hypertension and IHD were prescribed beta blockers. Of the 33 (13%) patients who were on beta-blockers, only 3 patients had an exacerbation of bronchial asthma symptoms. Cardioselective beta-blockers under supervision appear to be safe in patients with reactive airway disease and concomitant hypertension and IHD.

Keywords: beta blockers, hypertension, ischemic heart disease, asthma

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Authors: Youping Dai, Xinping Dai, Xiaoyun Li

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In this paper, the effect of Cosmic Background Gravitational Potential (CBGP) was discussed. It is helpful to reveal the equivalence of gravitational and inertial mass, and to understand the origin of inertia. The derivation is similar to the classic approach adopted by Landau in the book 'Classical Theory of Fields'.The main differences are that we used CBGP = Lambda^2 instead of c^2, and used CBGP energy E = m*Lambda^2 instead of kinetic energy E = (1/2)m*v^2 as initial assumptions (where Lambda has the same units for measuring velocity). It showed that Lorentz transformation, rest energy and Newtonian mechanics are all affected by $CBGP$, and the square of the speed of light is equal to CBGP too. Finally, the top value of cosmic mass density and cosmic radius were discussed.

Keywords: the origin of inertia, Mach's principle, equivalence principle, cosmic background potential

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Authors: Yonosuke Murayama

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We have developed and studied a metastable beta Ti alloy, which shows super-elasticity and low Young’s modulus according to the phase stability of its beta phase. The super-elasticity and low Young’s modulus are required in a wide range of applications in various industrial fields. For example, the metallic implant with low Young’s modulus and non-toxicity is desirable because the large difference of Young’s modulus between the human bone and the implant material may cause a stress-shielding phenomenon. We have investigated the role of Sn and Al in metastable beta Ti-Cr-Sn, Ti-Cr-Al, Ti-V-Sn, and Ti-V-Al alloys. The metastable beta Ti-Cr-Sn, Ti-Cr-Al, Ti-V-Sn, and Ti-V-Al alloys form during quenching from the beta field at high temperature. While Cr and V act as beta stabilizers, Sn and Al are considered as elements to suppress the athermal omega phase produced during quenching. The athermal omega phase degrades the properties of super-elasticity and Young’s modulus. Although Al and Sn as single elements are considered as an alpha stabilizer and neutral, respectively, Sn and Al acted also as beta stabilizers when added simultaneously with beta stabilized element of Cr or V in this experiment. The quenched microstructure of Ti-Cr-Sn, Ti-Cr-Al, Ti-V-Sn, and Ti-V-Al alloys shifts from martensitic structure to beta single-phase structure with increasing Cr or V. The Young’s modulus of Ti-Cr-Sn, Ti-Cr-Al, Ti-V-Sn, and Ti-V-Al alloys decreased and then increased with increasing Cr or V, each showing its own minimum value of Young's modulus respectively. The composition of the alloy with the minimum Young’s modulus is a near border composition where the quenched microstructure shifts from martensite to beta. The border composition of Ti-Cr-Sn and Ti-V-Sn alloys required only less amount of each beta stabilizer, Cr or V, than Ti-Cr-Al and Ti-V-Al alloys. This indicates that the effect of Sn as a beta stabilizer is stronger than Al. Sn and Al influenced the competitive relation between stress-induced martensitic transformation and slip deformation. Thus, super-elastic properties of metastable beta Ti-Cr-Sn, Ti-Cr-Al, Ti-V-Sn, and Ti-V-Al alloys varied depending on the alloyed element, Sn or Al.

Keywords: metastable beta Ti alloy, super-elasticity, low Young’s modulus, stress-induced martensitic transformation, beta stabilized element

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

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In this paper, we present the human action recognition method using the variational Bayesian HMM with the Dirichlet process mixture (DPM) of the Gaussian-Wishart emission model (GWEM). First, we define the Bayesian HMM based on the Dirichlet process, which allows an infinite number of Gaussian-Wishart components to support continuous emission observations. Second, we have considered an efficient variational Bayesian inference method that can be applied to drive the posterior distribution of hidden variables and model parameters for the proposed model based on training data. And then we have derived the predictive distribution that may be used to classify new action. Third, the paper proposes a process of extracting appropriate spatial-temporal feature vectors that can be used to recognize a wide range of human behaviors from input video image. Finally, we have conducted experiments that can evaluate the performance of the proposed method. The experimental results show that the method presented is more efficient with human action recognition than existing methods.

Keywords: human action recognition, Bayesian HMM, Dirichlet process mixture model, Gaussian-Wishart emission model, Variational Bayesian inference, prior distribution and approximate posterior distribution, KTH dataset

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Authors: Adam Abate, Elham Rasti, Philip Romero

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Beta-glucosidase is the key enzyme component present in cellulase and completes the final step during cellulose hydrolysis by converting the cellobiose to glucose. The regulatory properties of beta-glucosidases are most commonly found for the retaining and inverting enzymes. Hydrolysis of a glycoside typically occurs with general acid and general base assistance from two amino acid side chains, normally glutamic or aspartic acids. In order to obtain more detailed information on the dynamic events origination from the interaction with enzyme active site, we carried out molecular dynamics simulations of beta-glycosidase in protonated state (Glu-H178) and deprotonated state (Glu178). The theoretical models generated from our molecular dynamics simulations complement and advance the structural information currently available, leading to a more detailed understanding of Beta-glycosidase structure and function. This article presents the important role of Asn307 in enzyme activity of beta-glucosidase

Keywords: Beta-glucosidase, GROMACS, molecular dynamics simulation, structural parameters

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Authors: Saud Al Mahdi

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Traditionally,portfolio managers have been discouraged from timing the market. This means, for example, that equity managers have been forced to adhere strictly to a benchmark with static or relatively stable components, such as the SP 500 or the Russell 3000. This means that the portfolio’s exposures to all risk factors should mimic as closely as possible the corresponding exposures of the benchmark. The main risk factor, of course, is the market itself. Effectively, a long-only portfolio would be constrained to have a beta 1. More recently, however, managers have been given greater discretion to adjust their portfolio’s risk exposures (in particular, the beta of their portfolio) dynamically to match the manager’s beliefs about future performance of the risk factors themselves. This freedom translates into the manager’s ability to adjust the portfolio’s beta dynamically. These strategies have come to be known as smart beta strategies. Adjusting beta dynamically amounts to attempting to "time" the market; that is, to increase exposure when one anticipates that the market will rise, and to decrease it when one anticipates that the market will fall. Traditionally, market timing has been believed to be impossible to perform effectively and consistently. Moreover, if a majority of market participants do it, their combined actions could destabilize the market. The aim of this project is to investigate so-called smart beta strategies to determine if they really can add value, or if they are merely marketing gimmicks used to sell dubious investment strategies.

Keywords: beta, alpha, active portfolio management, trading strategies

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Authors: Jalil Qoulizadeh, Hasan Sadeghi

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Brain waves are electrical wave patterns that are produced in the human brain. Knowing these waves and activating them can have a positive effect on brain function and ultimately create an ideal life. The brain has the ability to produce waves from 0.1 to above 65 Hz. (The Beta One device produces exactly these waves) This is because it is said that the waves produced by the Beta One device exactly match the waves produced by the brain. The function and method of this device is based on the magnetic stimulation of the brain. The technology used in the design and producƟon of this device works in a way to strengthen and improve the frequencies of brain waves with a pre-defined algorithm according to the type of requested function, so that the person can access the expected functions in life activities. to perform better. The effect of this field on neurons and their stimulation: In order to evaluate the effect of this field created by the device, on the neurons, the main tests are by conducting electroencephalography before and after stimulation and comparing these two baselines by qEEG or quantitative electroencephalography method using paired t-test in 39 subjects. It confirms the significant effect of this field on the change of electrical activity recorded after 30 minutes of stimulation in all subjects. The Beta One device is able to induce the appropriate pattern of the expected functions in a soft and effective way to the brain in a healthy and effective way (exactly in accordance with the harmony of brain waves), the process of brain activities first to a normal state and then to a powerful one. Production of inexpensive neuroscience equipment (compared to existing rTMS equipment) Magnetic brain stimulation for clinics - homes - factories and companies - professional sports clubs.

Keywords: stimulation, brain, waves, betaOne

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Authors: Ha T. T. Ly, Truc B. Truc, Hai N. Truong, Mai P. T. Nguyen, Ngoc D. Ngo, Khanh V. Tran, Hai T. Le

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Beta thalassemia is one of the most common inherited blood disorders, which is characterized by decreased or absent in beta globin expression. Patients with Beta thalassemia whose anemia is not so severe as to necessitate transfusions are said to have thalassemia intermedia. Objective: The goal of this study is prenatal diagnosis for pregnancy woman with Beta thalassemia intermedia and her husband with Beta thalassemia carrier at high risk of Beta thalassemia major in Northern of Vietnam. Material and method: The family has a 6 years-old compound heterozygous thalassemia major for CD71/72(+A) and Hbb:c. -78A>G/nt-28(A>G) male child. The father was heterozygous for CD71/72(+A) mutation which is Beta plus type and the mother was compound heterozygosity of two different variants, namely, Hbb: c. -78A>G/nt-28(A>G) and CD26(A-G) HbE. Prenatal Beta thalassemia mutation detection in fetal DNA was carried out using multiplex Amplification-refractory mutation system ARMS-PCR and confirmed by direct Sanger-sequencing Hbb gene. Prenatal diagnoses were perfomed by amniotic fluid sampling from pregnant woman in the 16-18th week of pregnancy after the genotypes of parents of the probands were identified. Result: When amniotic fluid sample was analyzed for Beta globin gene (Hbb), we found that the genotype is heterozygous for CD71/72(+A) and CD26(A-G) HbE. This genotype is different from the 1st child of this family. Conclusion: Prenatal diagnosis helps the parents to know the genotype and the thalassemia status of the fetus, so they can have early decision on their pregnancy. Genetic diagnosis provided a useful method in diagnosis for familial members in pedigree, genetic counseling and prenatal diagnosis.

Keywords: beta thalassemia intermedia, Hbb gene, pedigree, prenatal diagnosis

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Authors: Wanhyun Cho, Soonja Kang, Sanggoon Kim, Soonyoung Park

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We present probabilistic multinomial Dirichlet classification model for multidimensional data and Gaussian process priors. Here, we have considered an efficient computational method that can be used to obtain the approximate posteriors for latent variables and parameters needed to define the multiclass Gaussian process classification model. We first investigated the process of inducing a posterior distribution for various parameters and latent function by using the variational Bayesian approximations and important sampling method, and next we derived a predictive distribution of latent function needed to classify new samples. The proposed model is applied to classify the synthetic multivariate dataset in order to verify the performance of our model. Experiment result shows that our model is more accurate than the other approximation methods.

Keywords: multinomial dirichlet classification model, Gaussian process priors, variational Bayesian approximation, importance sampling, approximate posterior distribution, marginal likelihood evidence

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Authors: Mario Gianni, Manuel A. Ruiz Garcia, Fiora Pirri

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In this work, we present a Bayesian non-parametric approach to model the motion control of ATVs. The motion control model is based on a Dirichlet Process-Gaussian Process (DP-GP) mixture model. The DP-GP mixture model provides a flexible representation of patterns of control manoeuvres along trajectories of different lengths and discretizations. The model also estimates the number of patterns, sufficient for modeling the dynamics of the ATV.

Keywords: Dirichlet processes, gaussian mixture models, learning motion patterns, tracked robots for urban search and rescue

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Authors: Phumelele Kubheka, Pius Owolawi, Gbolahan Aiyetoro

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Twitter is one of the most popular social media platforms where users can share their opinions on different subjects. As of 2010, The Twitter platform generates more than 12 Terabytes of data daily, ~ 4.3 petabytes in a single year. For this reason, Twitter is a great source for big mining data. Many industries such as Telecommunication companies can leverage the availability of Twitter data to better understand their markets and make an appropriate business decision. This study performs topic modeling on Twitter data using Latent Dirichlet Allocation (LDA). The obtained results are benchmarked with another topic modeling technique, Latent Semantic Indexing (LSI). The study aims to retrieve topics on a Twitter dataset containing user tweets on South African Telcos. Results from this study show that LSI is much faster than LDA. However, LDA yields better results with higher topic coherence by 8% for the best-performing model represented in Table 1. A higher topic coherence score indicates better performance of the model.

Keywords: big data, latent Dirichlet allocation, latent semantic indexing, telco, topic modeling, twitter

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Authors: Zahra Amirhosseini, Mahtab Nameni

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The aim of this study was to investigate the relationship between growth, beta, and Company's cash. We calculate cash as dependent variable and growth opportunity and beta as independent variables. This study was based on an analysis of panel data. Population of the study is the companies which listed in Tehran Stock exchange and a financial data of 215 companies during the period 2010 to 2015 have been selected as the sample through systematic sampling. The results of the first hypothesis showed there is a significant relationship between growth opportunities cash holdings. Also according to the analysis done in the second hypothesis, we determined that there is an inverse relation between company risk and cash holdings.

Keywords: growth, beta, liquidity, company

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Authors: Fuad Al Sarari

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The purpose of the present paper is to study subclasses of analytic functions which generalize the classes of Janowski functions introduced by Polatoglu. We study certain convolution conditions. This leads to a study of the sufficient condition and the neighborhood results related to the functions in the class S (T; H; F ): and a study of new subclasses of analytic functions that are defined using notions of the generalized Janowski classes and -symmetrical functions. In the quotient of analytical representations of starlikeness and convexity with respect to symmetric points, certain inherent properties are pointed out.

Keywords: convolution conditions, subordination, Janowski functions, starlike functions, convex functions

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Authors: K. Tejasri, K. Suvarna Vani, S. Prathyusha, S. Ramya

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Proteins are chained sequences of amino acids which are brought together by the peptide bonds. Many varying formations of the chains are possible due to multiple combinations of amino acids and rotation in numerous positions along the chain. Protein structure prediction is one of the crucial goals worked towards by the members of bioinformatics and theoretical chemistry backgrounds. Among the four different structure levels in proteins, we emphasize mainly the secondary level structure. Generally, the secondary protein basically comprises alpha-helix and beta-sheets. Multi-class classification problem of data with disparity is truly a challenge to overcome and has to be addressed for the beta strands. Imbalanced data distribution constitutes a couple of the classes of data having very limited training samples collated with other classes. The secondary structure data is extracted from the protein primary sequence, and the beta-strands are predicted using suitable machine learning algorithms.

Keywords: proteins, secondary structure elements, beta-sheets, beta-strands, alpha-helices, machine learning algorithms

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Authors: Sandeep Kaur Chouhan, Jatinderdeep Kaur, S. S. Bhatia

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The existence of sine and cosine series as a Fourier series, their L1-convergence seems to be one of the difficult question in theory of convergence of trigonometric series in L1-metric norm. In the literature so far available, various authors have studied the L1-convergence of cosine and sine trigonometric series with special coefficients. In this paper, we present a modified cosine and sine sums and criterion for L1-convergence of these modified sums is obtained. Also, a necessary and sufficient condition for the L1-convergence of the cosine and sine series is deduced as corollaries.

Keywords: conjugate Dirichlet kernel, Dirichlet kernel, L1-convergence, modified sums

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Authors: Aigul Manapova

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We consider an optimal control problem in the higher coefficient of nonlinear equations with a divergent elliptic operator and unbounded nonlinearity, and the Dirichlet boundary condition. The conditions imposed on the coefficients of the state equation are assumed to hold only in a small neighborhood of the exact solution to the original problem. This assumption suggests that the state equation involves nonlinearities of unlimited growth and considerably expands the class of admissible functions as solutions of the state equation. We obtain formulas for the first partial derivatives of the objective functional with respect to the control functions. To calculate the gradients the numerical solutions of the state and adjoint problems are used. We also prove that the gradient of the cost function is Lipchitz continuous.

Keywords: cost functional, differentiability, divergent elliptic operator, optimal control, unbounded nonlinearity

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Authors: Seyyed Payman Ziapour, Ahmadali Enayati, Sadegh Kheiri, Farzaneh Sahraei-Rostami, Reza Ali Mohammadpour, Mahmoud Fazeli-Dinan, Mohsen Aarabi, Fatemeh Asgarian, Seyed Hassan Nikookar, Mohammad Sarafrazi

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Rhipicephalus bursa (R. bursa) is a two-host ixodid tick with wide distribution in north of Iran especially in domestic animals of Mazandaran Province. The prolonged or incorrect use of chemical insecticides has led to build up of resistance in hard ticks in many areas of the world. Lack of basic information on resistance status of R. bursa was the reason behind this study to determine the susceptibility status of the species to lambda-cyhalothrin insecticide in Mazandaran Province. From May 2013 to March 2014, R. bursa ticks were collected on sheep, goat and cattle in different districts of Mazandaran Province. The engorged female ticks were reared in a controlled insectary for producing 12-18 days old larvae for larval packet test (LPT) bioassay against discriminant doses of lambda-cyhalothrin 5% EC (MAC SILAT®). 80% of ten pooled tick populations were susceptible to lambda-cyhalothrin as resistance ratios (RR50s) varied from 1 to 2.94 when compared with the most susceptible population NH-16. Only GK-12 and BF-6 populations (from plain areas of Galugah and Fereydunkenar Counties, respectively) were classified as resistant level I at LC50 level. Population NK-2 (from woodland areas of Kojour district in Nowshahr County) showed the highest resistance ratio of RR99 = 4.32 and 30% of tick populations were resistant at LC99 level. Our research showed initiation of lambda-cyhalothrin resistance in Rhipicephalus bursa populations in Mazandaran Province, Northern Iran. This is considered a warning to policy makers for disease control in the study area. This research is a part of the PhD thesis of SP. Ziapour by grant No. 92-89 in Student Research Committee, Mazandaran University of Medical Sciences, Iran.

Keywords: Rhipicephalus bursa, hard tick, lambda-cyhalothrin resistance, Iran

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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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