Commenced in January 2007
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Edition: International
Paper Count: 14

Search results for: Julia-wolf-caratéodory lemma

14 Extensions of Schwarz Lemma in the Half-Plane

Authors: Nicolae Pascu

Abstract:

Aside from being a fundamental tool in Complex analysis, Schwarz Lemma-which was finalized in its most complete form at the beginning of the last century-generated an important area of research in various fields of mathematics, which continues to advance even today. We present some properties of analytic functions in the half-plane which satisfy the conditions of the classical Schwarz Lemma (Carathéodory functions) and obtain a generalization of the well-known Aleksandrov-Sobolev Lemma for analytic functions in the half-plane (the correspondent of Schwarz-Pick Lemma from the unit disk). Using this Schwarz-type lemma, we obtain a characterization for the entire class of Carathéodory functions, which might be of independent interest. We prove two monotonicity properties for Carathéodory functions that do not depend upon their normalization at infinity (the hydrodynamic normalization). The method is based on conformal mapping arguments for analytic functions in the half-plane satisfying appropriate conditions, in the spirit of Schwarz lemma. According to the research findings in this paper, our main results give estimates for the modulus and the argument for the entire class of Carathéodory functions. As applications, we give several extensions of Julia-Wolf-Carathéodory Lemma in a half-strip and show that our results are sharp.

Keywords: schwarz lemma, Julia-wolf-caratéodory lemma, analytic function, normalization condition, caratéodory function

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13 Existence and Concentration of Solutions for a Class of Elliptic Partial Differential Equations Involving p-Biharmonic Operator

Authors: Debajyoti Choudhuri, Ratan Kumar Giri, Shesadev Pradhan

Abstract:

The perturbed nonlinear Schrodinger equation involving the p-biharmonic and the p-Laplacian operators involving a real valued parameter and a continuous real valued potential function defined over the N- dimensional Euclidean space has been considered. By the variational technique, an existence result pertaining to a nontrivial solution to this non-linear partial differential equation has been proposed. Further, by the Concentration lemma, the concentration of solutions to the same problem defined on the set consisting of those elements where the potential function vanishes as the real parameter approaches to infinity has been addressed.

Keywords: p-Laplacian, p-biharmonic, elliptic PDEs, Concentration lemma, Sobolev space

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12 The Grammatical Dictionary Compiler: A System for Kartvelian Languages

Authors: Liana Lortkipanidze, Nino Amirezashvili, Nino Javashvili

Abstract:

The purpose of the grammatical dictionary is to provide information on the morphological and syntactic characteristics of the basic word in the dictionary entry. The electronic grammatical dictionaries are used as a tool of automated morphological analysis for texts processing. The Georgian Grammatical Dictionary should contain grammatical information for each word: part of speech, type of declension/conjugation, grammatical forms of the word (paradigm), alternative variants of basic word/lemma. In this paper, we present the system for compiling the Georgian Grammatical Dictionary automatically. We propose dictionary-based methods for extending grammatical lexicons. The input lexicon contains only a few number of words with identical grammatical features. The extension is based on similarity measures between features of words; more precisely, we add words to the extended lexicons, which are similar to those, which are already in the grammatical dictionary. Our dictionaries are corpora-based, and for the compiling, we introduce the method for lemmatization of unknown words, i.e., words of which neither full form nor lemma is in the grammatical dictionary.

Keywords: acquisition of lexicon, Georgian grammatical dictionary, lemmatization rules, morphological processor

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11 The Automatisation of Dictionary-Based Annotation in a Parallel Corpus of Old English

Authors: Ana Elvira Ojanguren Lopez, Javier Martin Arista

Abstract:

The aims of this paper are to present the automatisation procedure adopted in the implementation of a parallel corpus of Old English, as well as, to assess the progress of automatisation with respect to tagging, annotation, and lemmatisation. The corpus consists of an aligned parallel text with word-for-word comparison Old English-English that provides the Old English segment with inflectional form tagging (gloss, lemma, category, and inflection) and lemma annotation (spelling, meaning, inflectional class, paradigm, word-formation and secondary sources). This parallel corpus is intended to fill a gap in the field of Old English, in which no parallel and/or lemmatised corpora are available, while the average amount of corpus annotation is low. With this background, this presentation has two main parts. The first part, which focuses on tagging and annotation, selects the layouts and fields of lexical databases that are relevant for these tasks. Most information used for the annotation of the corpus can be retrieved from the lexical and morphological database Nerthus and the database of secondary sources Freya. These are the sources of linguistic and metalinguistic information that will be used for the annotation of the lemmas of the corpus, including morphological and semantic aspects as well as the references to the secondary sources that deal with the lemmas in question. Although substantially adapted and re-interpreted, the lemmatised part of these databases draws on the standard dictionaries of Old English, including The Student's Dictionary of Anglo-Saxon, An Anglo-Saxon Dictionary, and A Concise Anglo-Saxon Dictionary. The second part of this paper deals with lemmatisation. It presents the lemmatiser Norna, which has been implemented on Filemaker software. It is based on a concordance and an index to the Dictionary of Old English Corpus, which comprises around three thousand texts and three million words. In its present state, the lemmatiser Norna can assign lemma to around 80% of textual forms on an automatic basis, by searching the index and the concordance for prefixes, stems and inflectional endings. The conclusions of this presentation insist on the limits of the automatisation of dictionary-based annotation in a parallel corpus. While the tagging and annotation are largely automatic even at the present stage, the automatisation of alignment is pending for future research. Lemmatisation and morphological tagging are expected to be fully automatic in the near future, once the database of secondary sources Freya and the lemmatiser Norna have been completed.

Keywords: corpus linguistics, historical linguistics, old English, parallel corpus

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10 Constant Factor Approximation Algorithm for p-Median Network Design Problem with Multiple Cable Types

Authors: Chaghoub Soraya, Zhang Xiaoyan

Abstract:

This research presents the first constant approximation algorithm to the p-median network design problem with multiple cable types. This problem was addressed with a single cable type and there is a bifactor approximation algorithm for the problem. To the best of our knowledge, the algorithm proposed in this paper is the first constant approximation algorithm for the p-median network design with multiple cable types. The addressed problem is a combination of two well studied problems which are p-median problem and network design problem. The introduced algorithm is a random sampling approximation algorithm of constant factor which is conceived by using some random sampling techniques form the literature. It is based on a redistribution Lemma from the literature and a steiner tree problem as a subproblem. This algorithm is simple, and it relies on the notions of random sampling and probability. The proposed approach gives an approximation solution with one constant ratio without violating any of the constraints, in contrast to the one proposed in the literature. This paper provides a (21 + 2)-approximation algorithm for the p-median network design problem with multiple cable types using random sampling techniques.

Keywords: approximation algorithms, buy-at-bulk, combinatorial optimization, network design, p-median

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9 B Spline Finite Element Method for Drifted Space Fractional Tempered Diffusion Equation

Authors: Ayan Chakraborty, BV. Rathish Kumar

Abstract:

Off-late many models in viscoelasticity, signal processing or anomalous diffusion equations are formulated in fractional calculus. Tempered fractional calculus is the generalization of fractional calculus and in the last few years several important partial differential equations occurring in the different field of science have been reconsidered in this term like diffusion wave equations, Schr$\ddot{o}$dinger equation and so on. In the present paper, a time-dependent tempered fractional diffusion equation of order $\gamma \in (0,1)$ with forcing function is considered. Existence, uniqueness, stability, and regularity of the solution has been proved. Crank-Nicolson discretization is used in the time direction. B spline finite element approximation is implemented. Generally, B-splines basis are useful for representing the geometry of a finite element model, interfacing a finite element analysis program. By utilizing this technique a priori space-time estimate in finite element analysis has been derived and we proved that the convergent order is $\mathcal{O}(h²+T²)$ where $h$ is the space step size and $T$ is the time. A couple of numerical examples have been presented to confirm the accuracy of theoretical results. Finally, we conclude that the studied method is useful for solving tempered fractional diffusion equations.

Keywords: B-spline finite element, error estimates, Gronwall's lemma, stability, tempered fractional

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8 New Variational Approach for Contrast Enhancement of Color Image

Authors: Wanhyun Cho, Seongchae Seo, Soonja Kang

Abstract:

In this work, we propose a variational technique for image contrast enhancement which utilizes global and local information around each pixel. The energy functional is defined by a weighted linear combination of three terms which are called on a local, a global contrast term and dispersion term. The first one is a local contrast term that can lead to improve the contrast of an input image by increasing the grey-level differences between each pixel and its neighboring to utilize contextual information around each pixel. The second one is global contrast term, which can lead to enhance a contrast of image by minimizing the difference between its empirical distribution function and a cumulative distribution function to make the probability distribution of pixel values becoming a symmetric distribution about median. The third one is a dispersion term that controls the departure between new pixel value and pixel value of original image while preserving original image characteristics as well as possible. Second, we derive the Euler-Lagrange equation for true image that can achieve the minimum of a proposed functional by using the fundamental lemma for the calculus of variations. And, we considered the procedure that this equation can be solved by using a gradient decent method, which is one of the dynamic approximation techniques. Finally, by conducting various experiments, we can demonstrate that the proposed method can enhance the contrast of colour images better than existing techniques.

Keywords: color image, contrast enhancement technique, variational approach, Euler-Lagrang equation, dynamic approximation method, EME measure

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7 Pricing, Production and Inventory Policies Manufacturing under Stochastic Demand and Continuous Prices

Authors: Masoud Rabbani, Majede Smizadeh, Hamed Farrokhi-Asl

Abstract:

We study jointly determining prices and production in a multiple period horizon under a general non-stationary stochastic demand with continuous prices. In some periods we need to increase capacity of production to satisfy demand. This paper presents a model to aid multi-period production capacity planning by quantifying the trade-off between product quality and production cost. The product quality is estimated as the statistical variation from the target performances obtained from the output tolerances of the production machines that manufacture the components. We consider different tolerance for different machines that use to increase capacity. The production cost is estimated as the total cost of owning and operating a production facility during the planning horizon.so capacity planning has cost that impact on price. Pricing products often turns out to be difficult to measure them because customers have a reservation price to pay that impact on price and demand. We decide to determine prices and production for periods after enhance capacity and consider reservation price to determine price. First we use an algorithm base on fuzzy set of the optimal objective function values to determine capacity planning by determine maximize interval from upper bound in minimum objectives and define weight for objectives. Then we try to determine inventory and pricing policies. We can use a lemma to solve a problem in MATLAB and find exact answer.

Keywords: price policy, inventory policy, capacity planning, product quality, epsilon -constraint

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6 Fault Tolerant (n, k)-Star Power Network Topology for Multi-Agent Communication in Automated Power Distribution Systems

Authors: Ning Gong, Michael Korostelev, Qiangguo Ren, Li Bai, Saroj Biswas, Frank Ferrese

Abstract:

This paper investigates the joint effect of the interconnected (n,k)-star network topology and Multi-Agent automated control on restoration and reconfiguration of power systems. With the increasing trend in development in Multi-Agent control technologies applied to power system reconfiguration in presence of faulty components or nodes. Fault tolerance is becoming an important challenge in the design processes of the distributed power system topology. Since the reconfiguration of a power system is performed by agent communication, the (n,k)-star interconnected network topology is studied and modeled in this paper to optimize the process of power reconfiguration. In this paper, we discuss the recently proposed (n,k)-star topology and examine its properties and advantages as compared to the traditional multi-bus power topologies. We design and simulate the topology model for distributed power system test cases. A related lemma based on the fault tolerance and conditional diagnosability properties is presented and proved both theoretically and practically. The conclusion is reached that (n,k)-star topology model has measurable advantages compared to standard bus power systems while exhibiting fault tolerance properties in power restoration, as well as showing efficiency when applied to power system route discovery.

Keywords: (n, k)-star topology, fault tolerance, conditional diagnosability, multi-agent system, automated power system

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5 Fault Tolerant (n,k)-star Power Network Topology for Multi-Agent Communication in Automated Power Distribution Systems

Authors: Ning Gong, Michael Korostelev, Qiangguo Ren, Li Bai, Saroj K. Biswas, Frank Ferrese

Abstract:

This paper investigates the joint effect of the interconnected (n,k)-star network topology and Multi-Agent automated control on restoration and reconfiguration of power systems. With the increasing trend in development in Multi-Agent control technologies applied to power system reconfiguration in presence of faulty components or nodes. Fault tolerance is becoming an important challenge in the design processes of the distributed power system topology. Since the reconfiguration of a power system is performed by agent communication, the (n,k)-star interconnected network topology is studied and modeled in this paper to optimize the process of power reconfiguration. In this paper, we discuss the recently proposed (n,k)-star topology and examine its properties and advantages as compared to the traditional multi-bus power topologies. We design and simulate the topology model for distributed power system test cases. A related lemma based on the fault tolerance and conditional diagnosability properties is presented and proved both theoretically and practically. The conclusion is reached that (n,k)-star topology model has measurable advantages compared to standard bus power systems while exhibiting fault tolerance properties in power restoration, as well as showing efficiency when applied to power system route discovery.

Keywords: (n, k)-star topology, fault tolerance, conditional diagnosability, multi-agent system, automated power system

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4 Adsorption of Phosphate from Aqueous Solution Using Filter Cake for Urban Wastewater Treatment

Authors: Girmaye Abebe, Brook Lemma

Abstract:

Adsorption of phosphorus (P as PO43-) in filter cake was studied to assess the media's capability in removing phosphorous from wastewaters. The composition of the filter cake that was generated from alum manufacturing process as waste residue has high amount of silicate from the complete silicate analysis of the experiment. Series of batches adsorption experiments were carried out to evaluate parameters that influence the adsorption capacity of PO43-. The factors studied include the effect of contact time, adsorbent dose, thermal pretreatment of the adsorbent, neutralization of the adsorbent, initial PO43- concentration, pH of the solution and effect of co-existing anions. Results showed that adsorption of PO43- is fairly rapid in first 5 min and after that it increases slowly to reach the equilibrium in about 1 h. The treatment efficiency of PO43- was increased with adsorbent extent. About 90% removal efficiency was increased within 1 h at an optimum adsorbent dose of 10 g/L for initial PO43- concentration of 10 mg/L. The amount of PO43- adsorbed increased with increasing initial PO43- concentration. Heat treatment and surface neutralization of the adsorbent did not improve the PO43- removal capacity and efficiency. The percentage of PO43- removal remains nearly constant within the pH range of 3-8. The adsorption data at ambient pH were well fitted to the Langmuir Isotherm and Dubinin–Radushkevick (D–R) isotherm model with a capacity of 25.84 and 157.55 mg/g of the adsorbent respectively. The adsorption kinetic was found to follow a pseudo-second-order rate equation with an average rate constant of 3.76 g.min−1.mg−1. The presence of bicarbonate or carbonate at higher concentrations (10–1000 mg/L) decreased the PO43- removal efficiency slightly while other anions (Cl-, SO42-, and NO3-) have no significant effect within the concentration range tested. The overall result shows that the filter cake is an efficient PO43- removing adsorbent against many parameters.

Keywords: wastewater, filter cake, adsorption capacity, phosphate (PO43-)

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3 Periodicity of Solutions to Impulsive Equations

Authors: Jin Liang, James H. Liu, Ti-Jun Xiao

Abstract:

It is known that there exist many physical phenomena where abrupt or impulsive changes occur either in the system dynamics, for example, ad-hoc network, or in the input forces containing impacts, for example, the bombardment of space antenna by micrometeorites. There are many other examples such as ultra high-speed optical signals over communication networks, the collision of particles, inventory control, government decisions, interest changes, changes in stock price, etc. These are impulsive phenomena. Hence, as a combination of the traditional initial value problems and the short-term perturbations whose duration can be negligible in comparison with the duration of the process, the systems with impulsive conditions (i.e., impulsive systems) are more realistic models for describing the impulsive phenomenon. Such a situation is also suitable for the delay systems, which include some of the past states of the system. So far, there have been a lot of research results in the study of impulsive systems with delay both in finite and infinite dimensional spaces. In this paper, we investigate the periodicity of solutions to the nonautonomous impulsive evolution equations with infinite delay in Banach spaces, where the coefficient operators (possibly unbounded) in the linear part depend on the time, which are impulsive systems in infinite dimensional spaces and come from the optimal control theory. It was indicated that the study of periodic solutions for these impulsive evolution equations with infinite delay was challenging because the fixed point theorems requiring some compactness conditions are not applicable to them due to the impulsive condition and the infinite delay. We are happy to report that after detailed analysis, we are able to combine the techniques developed in our previous papers, and some new ideas in this paper, to attack these impulsive evolution equations and derive periodic solutions. More specifically, by virtue of the related transition operator family (evolution family), we present a Poincaré operator given by the nonautonomous impulsive evolution system with infinite delay, and then show that the operator is a condensing operator with respect to Kuratowski's measure of non-compactness in a phase space by using an Amann's lemma. Finally, we derive periodic solutions from bounded solutions in view of the Sadovskii fixed point theorem. We also present a relationship between the boundedness and the periodicity of the solutions of the nonautonomous impulsive evolution system. The new results obtained here extend some earlier results in this area for evolution equations without impulsive conditions or without infinite delay.

Keywords: impulsive, nonautonomous evolution equation, optimal control, periodic solution

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2 Impact of Water Courses Lining on Water Quality and Distribution of Aquatic Vegetations in Two Egyptian Governorates

Authors: Nahed M. M. Ismail, Bayoumy B. Mostafa, Ahmed Abdel-Kader, Khalil M. El-Said, Asmaa Abdel-Motleb, Hoda M. Abu Taleb

Abstract:

This study was carried out in lined and unlined watercourses in Beheira and Giza governorates to investigate the effect of water canals lining on water quality and aquatic vegetations. Samples of water and aquatic plants were collected from the examining sites during four seasons in two successive years. The main ecological parameters were recorded and water quality was measured. Results showed that the mean value of water conductivity and total dissolved salts in lined sites was significantly lower than those of unlined ones (p < 0.01, p < 0.05). In Beheira, the dissolved oxygen concentrations during autumn and winter were higher in lined sites (3.93±1.3 and 9.6±1.1 ppm, respectively) than those of unlined ones (the same values of 1.2±0.6 ppm). However, it represented by lower values of 5.77±6.05 and 4.9±1.8 ppm in lined watercourses in spring and summer, respectively, comparing with those in unlined ones (14.05±5.59 and 5.83±0.8 ppm, respectively). Generally, Zn, Pb, Fe, Cd were higher in both lined and unlined sites during summer than the other seasons. However, Zn and Fe were higher in lined sites (0.78±0.37 and 17.4±4.3 ppb, respectively) during summer than that of unlined ones (0.4±0.1 and 10.95±1.93 ppb, respectively). Cu was absent during summer in lined and unlined sites and only in unlined ones during spring. Regarding to Giza sites, Cu and Pb were absent in both lined and unlined sites during summer and only in unlined ones during spring. Whereas, Fe recorded higher values in autumn in both lined (8.8±20.1 ppb) and unlined sites (15.16±3 ppb) than the other seasons. Present survey study revealed that 13 species of aquatic plants were collected from lined and unlined sites in Beheira and Giza governorates. Eichhornia crassipes, Ceratophyllum demersum, and Potamogeton sp. were the only plant species infested the examined sites during autumn and winter in Beheira. In autumn C. demersum was the only plant found in lined sites represented by highly lower significant percentage (12.5% of the all examined sites) compared to the unlined sites (50%). E. crassipes was completely absent in the lined sites during the two seasons. In spring, there is only 3 plant species in lined sites compared to 6 ones in unlined. Also, in summer, there is only 2 species in lined sites comparing with 5 in unlined. The percentage of occurrence and density of these plants was highly significant (p < 0.01, p < 0.001) higher in unlined sites compared to the lined ones during all seasons. A diversity of plant species, E. crassipes, C. demersum, Jussias repens, Lemma giba, and Polygonum serr were the most abundant in many examined sites during all seasons in Giza. In summer, the percentage of sites containing the two plants E. crassipes (83.3%) and C. demersum (50%) was highly significant (p < 0.001) higher in unlined sites compared to the lined ones (50% and 0.0%, respectively). It concluded from the results that watercourses lining may play a significant role in preserving water with a good quality and reduces the distribution of aquatic vegetation which rendered the current of water.

Keywords: aquatic plants, lining of watercourses, physicochemical parameters, water quality

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1 Challenges in the Last Mile of the Global Guinea Worm Eradication Program: A Systematic Review

Authors: Getahun Lemma

Abstract:

Introduction Guinea Worm Disease (GWD), also known as dracunculiasisis, is one of the oldest diseases in the history of mankind. Dracunculiasis is caused by a parasitic nematode, Dracunculus medinensis. Infection is acquired by drinking contaminated water with copepods containing infective Guinea Worm (GW) larvae). Almost one year after the infection, the worm usually emerges out through the skin on a lower, causing severe pain and disabilities. Although there is no effective drug or vaccine against the disease, the chain of transmission can be effectively prevented with simple and cost effective public health measures. Death due to dracunculiasis is very rare. However, it results in a wide range of physical, social and economic sequels. The disease is usually common in the rural, remote places of Sub-Saharan African countries among the marginalized societies. Currently, GWD is one of the neglected tropical diseases, which is on the verge of eradication. The global Guinea Worm Eradication Program (GWEP) was started in 1980. Since then, the program has achieved a tremendous success in reducing the global burden and number of GW case from 3.5 million to only 28 human cases at the end of 2018. However, it has recently been shown that not only humans can become infected, with a total of 1,105 animal infections have been reported at the end of 2018. Therefore, the objective of this study was to identify the existing challenges in the last mile of the GWEP in order To inform Policy makers and stakeholders on potential measures to finally achieve eradication. Method Systematic literature review on articles published from January 1, 2000 until May 30, 2019. Papers listed in Cochrane Library, Google Scholar, ProQuest PubMed and Web of Science databases were searched and reviewed. Results Twenty-five articles met inclusion criteria of the study and were selected for analysis. Hence, relevant data were extracted, grouped and descriptively analyzed. Results showed the main challenges complicating the last mile of global GWEP: 1. Unusual mode of transmission; 2. Rising animal Guinea Worm infection; 3. Suboptimal surveillance; 4. Insecurity; 5. Inaccessibility; 6. Inadequate safe water points; 7. Migration; 8. Poor case containment measures, 9. Ecological changes; and 10. New geographic foci of the disease. Conclusion This systematic review identified that most of the current challenges in the GWEP have been present since the start of the campaign. However, the recent change in epidemiological patterns and nature of GWD in the last remaining endemic countries illustrates a new twist in the global GWEP. Considering the complex nature of the current challenges, there seems to be a need for a more coordinated and multidisciplinary approach of GWD prevention and control measures in the last mile of the campaign. These new strategies would help to make history by eradicating dracunculiasis as the first ever parasitic disease.

Keywords: dracunculiasis, eradication program, guinea worm, last mile

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