Search results for: Positive solutions

Authors: Jose William Porras Ferreira

Abstract:

This paper presents two solutions to the Fermat’s Last Theorem (FLT). The first one using some algebraic basis related to the Pythagorean theorem, expression of equations, an analysis of their behavior, when compared with power  and power  and using " the “Well Ordering Principle” of natural numbers it is demonstrated that in Fermat equation . The second one solution is using the connection between  and power  through the Pascal’s triangle or  Newton’s binomial coefficients, where de Fermat equation do not fulfill the first coefficient, then it is impossible that:

zⁿ=xⁿ+yⁿ for n>2 and (x, y, z) E Z⁺ - {0}

 

Keywords: Fermat’s Last Theorem, Pythagorean Theorem, Newton Binomial Coefficients, Pascal’s Triangle, Well Ordering Principle.

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

Abstract:

The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

Keywords: Curved stretching sheet, finite difference method, MHD, variable thermal conductivity.

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Authors: Ismail El Gayar, Ossama Ismail, Yousri El Gamal

Abstract:

This paper presented a technique to solve one of the transportation problems that faces us in real life which is the Bus Scheduling Problem. Most of the countries using buses in schools, companies and traveling offices as an example to transfer multiple passengers from many places to specific place and vice versa. This transferring process can cost time and money, so we build a decision support system that can solve this problem. In this paper, a genetic algorithm with the shortest path technique is used to generate a competitive solution to other well-known techniques. It also presents a comparison between our solution and other solutions for this problem.

Keywords: Bus scheduling problem, decision support system, genetic algorithm, operation planning, shortest path, transportation.

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Authors: A. Ja, J. Belabid, A. Cheddadi

Abstract:

This paper reports the numerical simulation of doublediffusive natural convection flows within a horizontal annular filled with a saturated porous medium. The analysis concerns the influence of the different parameters governing the problem, namely, the Rayleigh number Ra, the Lewis number Le and the buoyancy ratio N, on the heat and mass transfer and on the flow structure, in the case of a fixed radius ratio R = 2. The numerical model used for the discretization of the dimensionless equations governing the problem is based on the finite difference method, using the ADI scheme. The study is focused on steady-state solutions in the cooperation situation.

Keywords: Natural convection, double-diffusion, porous medium, annular geometry, finite differences.

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Authors: Zilong Feng, Hong Li, Yang Liu, Siriguleng He

Abstract:

In this article, an adaptive least-squares mixed finite element method is studied for pseudo-parabolic integro-differential equations. The solutions of least-squares mixed weak formulation and mixed finite element are proved. A posteriori error estimator is constructed based on the least-squares functional and the posteriori errors are obtained.

Keywords: Pseudo-parabolic integro-differential equation, least squares mixed finite element method, adaptive method, a posteriori error estimates.

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Authors: N.A.Johan, S.R.M.Kutty, M. H. Isa, N.S.Muhamad, H.Hashim

Abstract:

Many non-conventional adsorbent have been studied as economic alternative to commercial activated carbon and mostly agricultural waste have been introduced such as rubber leaf powder and hazelnut shell. Microwave Incinerated Rice Husk Ash (MIRHA), produced from the rice husk is one of the low-cost materials that were used as adsorbent of heavy metal. The aim of this research was to study the feasibility of using MIRHA500 and MIRHA800 as adsorbent for the removal of Cu(II) metal ions from aqueous solutions by the batch studies. The adsorption of Cu(II) into MIRHA500 and MIRH800 favors Fruendlich isotherm and imply pseudo – kinetic second order which applied chemisorptions

Keywords: Copper (II) aqueous solution, batch study, MIRHA500, MIRHA800, Microwave Incinerated Rice Husk Ash(MIRHA)

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Authors: Marzieh Dosti, Alireza Nazemi

Abstract:

In this paper, the telegraph equation is solved numerically by cubic B-spline quasi-interpolation .We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable. The advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement. The results of numerical experiments are presented, and are compared with analytical solutions by calculating errors L2 and L∞ norms to confirm the good accuracy of the presented scheme.

Keywords: Cubic B-spline, quasi-interpolation, collocation method, second-order hyperbolic telegraph equation.

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Authors: Farnaz Nazem

Abstract:

This paper concentrates on the sustainable traditional architecture and urban planning in hot-humid regions of Iran. In a vast country such as Iran with different climatic zones traditional builders have presented series of logical solutions for human comfort. The aim of this paper is to demonstrate traditional architecture in hothumid climate of Iran as a sample of sustainable architecture. Iranian traditional architecture has been able to response to environmental problems for a long period of time. Its features are based on climatic factors, local construction materials of hot-humid regions and culture. This paper concludes that Iranian traditional architecture can be addressed as a sustainable architecture.

Keywords: Hot-humid climate, Iran, Sustainable Traditional architecture, Urban planning.

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Authors: Bin Cai, Shilong Wang, Haibo Hu

Abstract:

The job shop scheduling problem (JSSP) is well known as one of the most difficult combinatorial optimization problems. This paper presents a hybrid genetic algorithm for the JSSP with the objective of minimizing makespan. The efficiency of the genetic algorithm is enhanced by integrating it with a local search method. The chromosome representation of the problem is based on operations. Schedules are constructed using a procedure that generates full active schedules. In each generation, a local search heuristic based on Nowicki and Smutnicki-s neighborhood is applied to improve the solutions. The approach is tested on a set of standard instances taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm.

Keywords: Genetic algorithm, Job shop scheduling problem, Local search, Meta-heuristic algorithm

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Authors: Eduardo da Silva, Tânia Caetano, Jessica B. Lopes

Abstract:

Emotion dysregulation has been linked to psychopathology in general and, in particular, to substance abuse and other addiction-related disorders, such as eating disorders, impulsive disorder, and gambling. It has been proposed that a lessening of the difficulties in emotion regulation can have a significant positive impact on the treatment of these disorders. The present study explores the association between the progress in the Change & Grow^® therapeutic model (5 stages of treatment), and the decrease in the difficulties related to emotion regulation. The Change & Grow^® model has five stages of treatment according to the model’s five principles (Truth, Acceptance, Gratitude, Love and Responsibility) and incorporates different therapeutic approaches such as positive psychology, cognitive and behavioral therapy and third generation therapies. The main objective is to understand the impact of the presented therapeutic model on difficulties in emotion regulation in patients with addiction-related disorders. The exploratory study has a cross-sectional design. Participants were 44 (15 women and 29 men) Portuguese patients in the residential Villa Ramadas International Treatment Centre. The instrument used was the Portuguese version of the Difficulties in Emotion Regulation Scale (DERS), which measures six dimensions of emotion regulation (Strategies, Non-acceptance, Awareness, Impulse, Goals, and Clarity). The mean rank scores for both the DERS total score and the Impulse subscale showed statistically significant differences according to Stage of Treatment/Principles. Furthermore, Stage of Treatment/Principles held a negative correlation with the scores of the Non-acceptance and Impulse subscales, as well as the DERS total score. The results indicate that the Change & Grow^® model seems to have an impact in lessening the patient’s difficulties in emotion regulation. The Impulse dimension suffered the greater impact, which supports the well-known relevance of impulse control, or related difficulties, in addiction-related disorders.

Keywords: Addiction, Change & Grow®, emotion regulation, psychopathology.

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Authors: Suttijit Sriwatcharakul

Abstract:

The bioactivity studies from the weed ethanolic crude extracts from leaf, stem, pod and root of wild spider flower; Cleoma viscosa Linn. were analyzed for the growth inhibition of 6 bacterial species; Salmonella typhimurium TISTR 5562, Pseudomonas aeruginosa ATCC 27853, Staphylococcus aureus TISTR 1466, Streptococcus epidermidis ATCC 1228, Escherichia coli DMST 4212 and Bacillus subtilis ATCC 6633 with initial concentration crude extract of 50 mg/ml. The agar well diffusion results found that the extracts inhibit only gram positive bacteria species; S. aureus, S. epidermidis and B. subtilis. The minimum inhibition concentration study with gram positive strains revealed that leaf crude extract give the best result of the lowest concentration compared with other plant parts to inhibit the growth of S. aureus, S. epidermidis and B. subtilis at 0.78, 0.39 and lower than 0.39 mg/ml, respectively. The determination of total phenolic compounds in the crude extracts exhibited the highest phenolic content was 10.41 mg GAE/g dry weight in leaf crude extract. Analyzed the efficacy of free radical scavenging by using DPPH radical scavenging assay with all crude extracts showed value of IC50 of leaf, stem, pod and root crude extracts were 8.32, 12.26, 21.62 and 35.99 mg/ml, respectively. Studied cytotoxicity of crude extracts on human breast adenocarcinoma cell line by MTT assay found that pod extract had the most cytotoxicity CC50 value, 32.41 µg/ml. Antioxidant activity and cytotoxicity of crude extracts exhibited that the more increase of extract concentration, the more activities indicated. According to the bioactivities results, the leaf crude extract of Cleoma viscosa Linn. is the most interesting plant part for further work to search the beneficial of this weed.

Keywords: Antimicrobial, antioxidant activity, Cleoma viscosa Linn., cytotoxicity test, total phenolic compound.

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Authors: Marzieh Dosti, Alireza Nazemi

Abstract:

Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.

Keywords: B-spline, collocation method, second-order hyperbolic telegraph equation, difference schemes.

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Authors: Achim Kampker, Peter Burggräf, Moritz Krunke, Hanno Voet

Abstract:

As a reaction to current challenges in factory planning, many companies think about introducing factory standards to lower planning times and decrease planning costs. If these factory standards are set-up with a high level of modularity, they are defined as modular factory systems. This paper deals with the main current problems in the application of modular factory systems in practice and presents a solution approach with its basic models. The methodology is based on methods from factory planning but also uses the tools of other disciplines like product development or technology management to deal with the high complexity, which the development of modular factory systems implies. The four basic models that such a methodology has to contain are introduced and pointed out.

Keywords: Factory planning, modular factory systems, factory standards, cost-benefit analysis.

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Authors: Jain-Shing Liu

Abstract:

In this work, we study the problem of determining the minimum scheduling length that can satisfy end-to-end (ETE) traffic demand in scheduling-based multihop WSNs with cooperative multiple-input multiple-output (MIMO) transmission scheme. Specifically, we present a cross-layer formulation for the joint routing, scheduling and stream control problem by incorporating various power and rate adaptation schemes, and taking into account an antenna beam pattern model and the signal-to-interference-and-noise (SINR) constraint at the receiver. In the context, we also propose column generation (CG) solutions to get rid of the complexity requiring the enumeration of all possible sets of scheduling links.

Keywords: Wireless Sensor Networks, Cross-Layer Design, CooperativeMIMO System, Column Generation.

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Authors: M. Nassereddine, J. Rizk, M. Nagrial

Abstract:

Green house effect has becomes a serious concern in many countries due to the increase consumption of the fossil fuel. There have been many studies to find an alternative power source. Wind energy found to be one of the most useful solutions to help in overcoming the air pollution and global. There is no agreed solution to conversion of wind energy to electrical energy. In this paper, the advantages of using a Switched Reluctance Generator (SRG) for wind energy applications. The theoretical study of the self excitation of a SRG and the determination of the variable parameters in a SRG design are discussed. The design parameters for the maximum power output of the SRG are computed using Matlab simulation. The designs of the circuit to control the variable parameters in a SRG to provide the maximum power output are also discussed.

Keywords: Switched Reluctance Generator, Wind Power, Electrical Machines.

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Authors: C. E. Nugraheni, L. Abednego

Abstract:

This paper introduces a framework based on the collaboration of multi agent and hyper-heuristics to find a solution of the real single machine production problem. There are many techniques used to solve this problem. Each of it has its own advantages and disadvantages. By the collaboration of multi agent system and hyper-heuristics, we can get more optimal solution. The hyper-heuristics approach operates on a search space of heuristics rather than directly on a search space of solutions. The proposed framework consists of some agents, i.e. problem agent, trainer agent, algorithm agent (GPHH, GAHH, and SAHH), optimizer agent, and solver agent. Some low level heuristics used in this paper are MRT, SPT, LPT, EDD, LDD, and MON

Keywords: Hyper-heuristics, multi-agent systems, scheduling problem.

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Authors: Hiroshi Katanoda, Mohd Hazwan bin Yusof

Abstract:

A theoretical investigation from the view point of gas-dynamics and thermodynamics was carried out, in order to clarify the energy separation mechanism in a viscous compressible vortex, as a primary flow element in a uni-flow vortex tube. The mathematical solutions of tangential velocity, density and temperature in a viscous compressible vortical flow were used in this study.It is clear that a total temperature in the vortex core falls well below that distant from the vortex core in the radial direction, causing aregion with higher total temperature,compared to the distant region,peripheral to the vortex core.

Keywords: Energy separation mechanism, theoretical analysis, vortex tube, vortical flow.

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Authors: Germán Santos-Boada, Jordi Domingo-Pascual

Abstract:

Recently, in some places, optical-fibre access networks have been used with GPON technology belonging to organizations (in most cases public bodies) that act as neutral operators. These operators simultaneously provide network services to various telecommunications operators that offer integrated voice, data and television services. This situation creates new problems related to quality of service, since the interests of the users are intermingled with the interests of the operators. In this paper, we analyse this problem and consider solutions that make it possible to provide guaranteed quality of service for voice over IP, data services and interactive digital television.

Keywords: GPON networks, multioperator, quality of service, triple-play services.

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Authors: Amin Almasi

Abstract:

Reliability assessment and risk analysis of rotating machine rotors in various overload and malfunction situations present challenge to engineers and operators. In this paper a new analytical method for evaluation of rotor under large deformation is addressed. Model is presented in general form to include also composite rotors. Presented simulation procedure is based on variational work method and has capability to account for geometric nonlinearity, large displacement, nonlinear support effect and rotor contacting other machine components. New shape functions are presented which capable to predict accurate nonlinear profile of rotor. The closed form solutions for various operating and malfunction situations are expressed. Analytical simulation results are discussed

Keywords: Large Deformation, Nonlinear, Rotor.

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Authors: E. Assareh, M.A. Behrang, M. Ghalambaz, A.R. Noghrehabadi, A. Ghanbarzadeh

Abstract:

In this paper, a new approach is introduced to solve Blasius equation using parameter identification of a nonlinear function which is used as approximation function. Bees Algorithm (BA) is applied in order to find the adjustable parameters of approximation function regarding minimizing a fitness function including these parameters (i.e. adjustable parameters). These parameters are determined how the approximation function has to satisfy the boundary conditions. In order to demonstrate the presented method, the obtained results are compared with another numerical method. Present method can be easily extended to solve a wide range of problems.

Keywords: Bees Algorithm (BA); Approximate Solutions; Blasius Differential Equation.

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Authors: Alexander B. Bichkov, Alla A. Mityureva, Valery V. Smirnov

Abstract:

In present work are considered the scheme of evaluation the transition probability in quantum system. It is based on path integral representation of transition probability amplitude and its evaluation by means of a saddle point method, applied to the part of integration variables. The whole integration process is reduced to initial value problem solutions of Hamilton equations with a random initial phase point. The scheme is related to the semiclassical initial value representation approaches using great number of trajectories. In contrast to them from total set of generated phase paths only one path for each initial coordinate value is selected in Monte Karlo process.

Keywords: Path integral, saddle point method, semiclassical approximation, transition probability

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Authors: M. Lamri Zeggar, F. Bourfaa, A. Adjimi, F. Boutbakh, M. S. Aida, N. Attaf

Abstract:

CuO thin films were deposited by spray ultrasonic pyrolysis with different precursor solution. Two staring solution slats were used namely: copper acetate and copper chloride. The influence of these solutions on CuO thin films proprieties of is instigated. The X rays diffraction (XDR) analysis indicated that the films deposed with copper acetate are amorphous however the films elaborated with copper chloride have monoclinic structure. UV- Visible transmission spectra showed a strong absorbance of the deposited CuO thin films in the visible region. Electrical characterization has shown that CuO thin films prepared with copper acetate have a higher electrical conductivity.

Keywords: Thin films, cuprous oxide, spray pyrolysis, precursor solution.

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Authors: Ahmad Munawar

Abstract:

The provision of urban public transport in Indonesia is not free of problems. Some of the problems include: an overall lack of capacity, lack of quality and choice, severe traffic congestions and insufficient fund to renew and repair vehicles. Generally, the comfort and quality of the city bus is poor, and many of the vehicles are dilapidated and dirty. Surveys were carried out in the city of Yogyakarta, by counting city bus vehicles and occupancies, interviewing the bus passengers, drivers and institutional staffs, who involve in public transport management. This paper will then analyze the possible plan to develop the public transport system to become more attractive and to improve the public transport management. The short, medium and long term plans are analyzed, to find the best solutions. Some constraints such as social impacts and financial impact are also taken into accounts.

Keywords: City bus, management, public transport.

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Authors: Zia Amjad, Salem S. Alghamdi

Abstract:

The study was conducted at the student educational farm at the College of Food and Agriculture in the Kingdom of Saudi Arabia. The aim of study was to characterize 154 Vicia faba L. accessions using agro-morphological traits based on The International Union for the Protection of New Varieties of Plants (UPOV) and The International Board for Plant Genetic Resources (IBPGR) descriptors. This research is significant as it contributes to the understanding of the genetic diversity and potential yield of V. faba in Saudi Arabia. In the study, 24 agro-morphological characters including 11 quantitative and 13 qualitative were observed for genetic variation. All the results were analyzed using multivariate analysis i.e., principal component analysis (PCA). First, six principal components (PC) had eigenvalues greater than one; accounted for 72% of available V. faba genetic diversity. However, first three components revealed more than 10% of genetic diversity each i.e., 22.36%, 15.86% and 10.89% respectively. PCA distributed the V. faba accessions into different groups based on their performance for the characters under observation. PC-1, which represented 22.36% of the genetic diversity, was positively associated with stipule spot pigmentation, intensity of streaks, pod degree of curvature and to some extent with 100 seed weight. PC-2 covered 15.86 of the genetic diversity and showed positive association for average seed weight per plant, pod length, number of seeds per plant, 100 seed weight, stipule spot pigmentation, intensity of streaks (same as in PC-1) and to some extent for pod degree of curvature and number of pods per plant. PC-3 revealed 10.89% of genetic diversity and expressed positive association for number of pods per plant and number of leaflets per plant. This study contributes to the understanding of the genetic diversity and potential yield of V. faba in the Kingdom of Saudi Arabia. By establishing a core collection of V. faba, the research provides a valuable resource for future conservation and utilization of this crop worldwide.

Keywords: Agro-morphological characterization, genetic diversity, core collection, PCA, Vicia faba L.

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Authors: Zhenhuan Zhu, David Mulvaney, Vassilios Chouliaras

Abstract:

This paper presents a novel genetic algorithm, termed the Optimum Individual Monogenetic Algorithm (OIMGA) and describes its hardware implementation. As the monogenetic strategy retains only the optimum individual, the memory requirement is dramatically reduced and no crossover circuitry is needed, thereby ensuring the requisite silicon area is kept to a minimum. Consequently, depending on application requirements, OIMGA allows the investigation of solutions that warrant either larger GA populations or individuals of greater length. The results given in this paper demonstrate that both the performance of OIMGA and its convergence time are superior to those of existing hardware GA implementations. Local convergence is achieved in OIMGA by retaining elite individuals, while population diversity is ensured by continually searching for the best individuals in fresh regions of the search space.

Keywords: Genetic algorithms, hardware-based machinelearning.

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Authors: Y. Saylan, F. Yılmaz, A. Denizli

Abstract:

In this study, we have focused our attention on combining of molecular imprinting into nanofilms and QCM nanosensor approaches and producing QCM nanosensor for anti- CCP, chosen as model protein, using anti-CCP imprinted nanofilms. The nonimprinted nanosensor was also prepared to evaluate the selectivity of the imprinted nanosensor. Anti-CCP imprinted QCM nanosensor was tested for real time detection of anti-CCP from aqueous solution. The kinetic and affinity studies were determined by using anti-CCP solutions with different concentrations. The responses related with mass shifts (%m) and frequency shifts (%f) were used to evaluate adsorption properties. To show the selectivity of the anti-CCP imprinted QCM nanosensor, competitive adsorption of anti-CCP and IgM was investigated. The results indicate that anti- CCP imprinted QCM nanosensor has higher adsorption capabilities for anti-CCP than for IgM, due to selective cavities in the polymer structure.

Keywords: Anti-CCP, molecular imprinting, QCM nanosensor, rheumatoid arthritis.

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Authors: A. Faro, D. Giordano, M. Pennisi, G. Scarciofalo, C. Spampinato, F. Tramontana

Abstract:

The paper proposes a methodology to process the signals coming from the Transcranial Magnetic Stimulation (TMS) in order to identify the pathology and evaluate the therapy to treat the patients affected by demency diseases. In particular, a fuzzy model is developed to identify the demency of the patients affected by Subcortical Ischemic Vascular Dementia and to measure the positive effect, if any, of a repetitive TMS on their motor performances. A tool is also presented to support the mentioned analysis.

Keywords: TMS, SIVD, Electromiography , Fuzzy Logic.

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Authors: Hamid Reza Pakzad

Abstract:

Ion-acoustic solitary waves in a plasma with nonthermal electrons, thermal positrons and warm ions are investigated using Sagdeev-s pseudopotential technique. We study the effects of non-thermal electrons and ion temperature on solitons and show both negative and positive potential waves are possible.

Keywords: Ion acoustic waves, Solitons, Nonlinear phenomena, Sagdeev potential

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Authors: Manuel A. Alonso-Tarajano, Roberto Mosca, Patrick Aloy

Abstract:

Protein kinases participate in a myriad of cellular processes of major biomedical interest. The in vivo substrate specificity of these enzymes is a process determined by several factors, and despite several years of research on the topic, is still far from being totally understood. In the present work, we have quantified the contributions to the kinase substrate specificity of i) the phosphorylation sites and their surrounding residues in the sequence and of ii) the association of kinases to adaptor or scaffold proteins. We have used position-specific scoring matrices (PSSMs), to represent the stretches of sequences phosphorylated by 93 families of kinases. We have found negative correlations between the number of sequences from which a PSSM is generated and the statistical significance and the performance of that PSSM. Using a subset of 22 statistically significant PSSMs, we have identified specificity determinant residues (SDRs) for 86% of the corresponding kinase families. Our results suggest that different SDRs can function as positive or negative elements of substrate recognition by the different families of kinases. Additionally, we have found that human proteins with known function as adaptors or scaffolds (kAS) tend to interact with a significantly large fraction of the substrates of the kinases to which they associate. Based on this characteristic we have identified a set of 279 potential adaptors/scaffolds (pAS) for human kinases, which is enriched in Pfam domains and functional terms tightly related to the proposed function. Moreover, our results show that for 74.6% of the kinase–pAS association found, the pAS colocalize with the substrates of the kinases they are associated to. Finally, we have found evidence suggesting that the association of kinases to adaptors and scaffolds, may contribute significantly to diminish the in vivo substrate crossed-specificity of protein kinases. In general, our results indicate the relevance of several SDRs for both the positive and negative selection of phosphorylation sites by kinase families and also suggest that the association of kinases to pAS proteins may be an important factor for the localization of the enzymes with their set of substrates.

Keywords: Kinase, phosphorylation, substrate specificity, adaptors, scaffolds, cellular colocalization.

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Authors: A. M. Sagir

Abstract:

In this paper, self-starting block hybrid method of order (5,5,5,5)T is proposed for the solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on stiff ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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