Search results for: differential haemocyte count (DHC)

Authors: Fouzia Qamar, Shahida Hasnain

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The present study is primarily concerned with the alteration in haemocyte profile of adult male Periplaneta americana with emphasis on the effect of bacterial inoculations on the haemogram i.e., total haemocyte count (THC) and differential haemocyte count (DHC) of different haemocyte types of the target insect. Haemolymph cellular profile showed considerable alterations under the effect of nine strains of Agrobacterium tumefaciens after 8, 16 and 24 hrs of treatment thereby signifying the potential role of Agrobacterium tumefaciens as a possible biocontrol agent against the house hold pests.

Keywords: Agrobacterium tumefaciens, Periplaneta americana, Haemolymph, cellular parametes

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Authors: Muhammad Zaheer Awan, Adnan Qadir, Zeeshan Anjum

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Housefly, Musca domestica Linnaeus is ubiquitous and hazardous for Homo sapiens and livestock in sundry venerations. Musca domestica cart 100 different pathogens, such as typhoid, salmonella, bacillary dysentery, tuberculosis, anthrax and parasitic worms. The flies in rural areas usually carry more pathogens. Houseflies feed on liquid or semi-liquid substances besides solid materials which are softened by saliva. Neem botanically known as Azadirachta indica belongs to the family Meliaceae and is an indigenous tree to Pakistan. The neem tree is also one such tree which has been revered by the Pakistanis and Kashmiris for its medicinal properties. Present study showed neem seed extract has potentially toxic ability that affect Total Haemocyte Count (THC) and Differential Haemocytes Count (DHC) in insect’s blood cells, of the housefly. A significant variation in haemolymph density was observed just after application, 30 minutes and 60 minutes post treatment in term of THC and DHC in comparison with novastar. The study strappingly acclaim use of neem seed extract as insecticide as compare to artificial insecticides.

Keywords: neem, Azadirachta indica, Musca domestica, differential haemocyte count (DHC), total haemocytes count (DHC), novastar

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Authors: Gian Carlo F. Maliwat, Stephanie F. Velasquez, Janice A. Ragaza

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A 50-day growth trial was conducted to evaluate the efficacy of Chlorella vulgaris (Beijerinck) as an ingredient in the diets of giant freshwater prawn Macrobrachium rosenbergii (De Man) postlarvae (PL30). Immune response (total haemocyte count and prophenoloxidase activity) was also assessed by subjecting postlarvae to a challenge test against Aeromonas hydrophila (Chester) for 14 days. Isonitrogenous and iso-lipidic test diets were prepared using a fishmeal-based-positive control diet (D0) and four basal diets with inclusion levels of 2% (D2), 4% (D4), 6% (D6) and 8% (D8) C. vulgaris. Postlarvae of M. rosenbergii were randomly stocked (mean initial body weight of 0.19 ± 0.02 g) in 30-L tanks in three replicates per dietary treatment for evaluation of growth performance. Another set of postlarvae (mean initial body weight of 1.25 ± 0.02 g) was randomly distributed in 95-L tanks in three replicates per dietary treatment for the assessment of immune response. Results showed that specific growth rate was significantly higher (P < 0.05) in postlarvae fed D4 and D6. Variations in values for carcass protein, lipid, moisture, and ash were also evident. Postlarvae fed diets with Chlorella showed increased prophenol oxidase activity and total haemocyte counts. Moreover, the survival rate after challenge with A. hydrophila was significantly increased (P < 0.05). Inclusion of C. vulgaris in diets enhanced immune response and resistance of M. rosenbergii postlarvae against A. hydrophila infection.

Keywords: Chlorella vulgaris, haemocyte count, Macrobrachium rosenbergii, prophenoloxidase activity

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Authors: Fatima Zohra Bissaad, Farid Bounaceur, Nassima Behidj, Nadjiba Chebouti, Fatma Halouane, Bahia Doumandji-Mitiche

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Effect of Beauveria bassiana and Metarhizium anisopliae var. acridum on the 5^th instar nymphs of Schistocerca gregaria was studied in the laboratory. Infection by these both entomopathogenic fungi caused reduction in the hemolymph total protein. The average amounts of total proteins were 2.3, 2.07, 2.09 µg/100 ml of haemolymph in the control and M. anisopliae var. acridum, and B. bassiana based-treatments, respectively. Three types of haemocytes were recognized and identified as prohaemocytes, plasmatocytes and granulocytes. The treatment caused significant reduction in the total haemocyte count and in each haemocyte type on the 9^th day after its application.

Keywords: Beauveria bassiana, haemolymph picture, haemolymph protein, Metarhizium anisopliae var. acridum, Schistocerca gregaria

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Authors: Ibtisam Masmali, Edwin Beggs

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In this paper, we take example of differential calculi, on the finite group A4. Then, we apply methods of non-commutative of non-commutative differential geometry to this example, and see how similar the results are to those of classical differential geometry.

Keywords: differential calculi, finite group A4, Christoffel symbols, covariant derivative, torsion compatible

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Authors: Ines Kovacic, Dijana Pavicic-Hamer, Petra Buric, Maja Levak Zorinc, Daniel M. Lyons

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Silver nanoparticles (AgNPs), owing to their unique physical and chemical properties, have become one of the most widely used nanoparticles in consumer products. Despite the increased use of AgNPs in science and industry over the past twenty years, only relatively recently has concern been raised over their entering brackish and marine environments. However, data on their potential impact on marine organisms, especially invertebrates are very limited. This study aimed to examine the effects of 60 nm AgNPs (10, 100, 500 and 1000 µg/l) and silver ions (100, 1000 µg/l) on the Mediterranean green crab Carcinus aestuarii Nardo, 1847. The crab mortality was assessed during seven days of exposure. After the exposure, total haemocytes (THC) and differential haemocytes number (DHC) were counted (immune response), in addition to histological examination of gills stained with haematoxylin and eosin. The effect of AgNPs and silver ions resulted in a dose dependent mortality and destruction of gills epithelium with haemocytes infiltration in the gills lacuna. Total haemocyte count was greater with increasing concentration of AgNPs, at concentrations from 10 to 500 µg/l. Hyalinocytes were the most common immunological cells noted in the crab hemolymph, while granulocytes and semigranulocytes were suppressed with increasing concentration of AgNPs (500 and 1000 µg/l). Thus, as crabs are filter feeders, they are susceptible to uptake of AgNPs by direct accumulation in gills mucus or indirectly via circulation of haemocytes in their open vascular system. Results of this study on crabs add to knowledge of the effects of AgNPs in the marine environment.

Keywords: crab, immune response, histological alteration, silver nanoparticles

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Authors: Paula Simões, Isabel Natário

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This paper reviews a number of theoretical aspects for implementing an explicit spatial perspective in econometrics for modelling non-continuous data, in general, and count data, in particular. It provides an overview of the several spatial econometric approaches that are available to model data that are collected with reference to location in space, from the classical spatial econometrics approaches to the recent developments on spatial econometrics to model count data, in a Bayesian hierarchical setting. Considerable attention is paid to the inferential framework, necessary for structural consistent spatial econometric count models, incorporating spatial lag autocorrelation, to the corresponding estimation and testing procedures for different assumptions, to the constrains and implications embedded in the various specifications in the literature. This review combines insights from the classical spatial econometrics literature as well as from hierarchical modeling and analysis of spatial data, in order to look for new possible directions on the processing of count data, in a spatial hierarchical Bayesian econometric context.

Keywords: spatial data analysis, spatial econometrics, Bayesian hierarchical models, count data

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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Authors: Ramutė Miseikienė, Saulius Tusas

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Somatic cell count and bacteria count are the main indicators of cow milk quality. The aim of this study was to analyze and compare parameters of milk quality in different-sized cows herds. Milk quality of ten dairy cows farms during one year period was analyzed. Dairy farms were divided into five groups according to number of cows in the farm (under 50 cows, 51–100 cows, 101–200 cows, 201–400 cows and more than 400 cows). The averages of somatic cells bacteria count in milk and milk freezing temperature were analyzed. Also, these parameters of milk quality were compared during outdoor (from May to September) and indoor (from October to April) periods. The largest number of SCC was established in the smallest farms, i.e., in farms under 50 cows and 51-100 cows (respectively 264±9,19 and 300±10,24 thousand/ml). Reliable link between the smallest and largest dairy farms and farms with 101-200 and 201-400 cows and count of somatic cells in milk has not been established (P > 0.05). Bacteria count had a low tendency to decrease when the number of cows in farms increased. The highest bacteria number was determined in the farms with 51-100 cows and the the lowest bacteria count was in milk when 201-400 and more than 401 cows were kept. With increasing the number of cows milk maximal freezing temperature decreases (significant negative trend), i. e, indicator is improving. It should be noted that in all farms milk freezing point never exceeded requirements (-0.515 °C). The highest difference between SCC in milk during the indoor and outdoor periods was established in farms with 201-400 cows (respectively 218.49 thousand/ml and 268.84 thousand/ml). However, the count of SC was significantly higher (P < 0.05) during outdoor period in large farms (201-400 and more cows). There was no significant difference between bacteria count in milk during both – outdoor and indoor – periods (P > 0.05).

Keywords: bacteria, cow, farm size, somatic cell count

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Authors: Imene Soufli, Abdelkrim Hablal, Manel Amri, Moussa Labsi, Rania Sihem Boussa, Nassim Sid Idris, Chafia Touil-Boukoffa

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Crohn’s Disease (CD) is a relapsing–remitting inflammatory bowel disease with a progressive course. The aim of our study was to evaluate the relationship between the immunomarkers: Nitric Oxide (NO), pro-inflammatory cytokines, and blood count-based ratios and the outcome of corticosteroid or anti-TNF-α therapy in patients with complicated Crohn’s Disease. In this context, we evaluated the NLR as the ratio of neutrophil count to lymphocyte count, PLR as the ratio of platelet counts to lymphocyte count, and MLR as the ratio of monocyte count to lymphocyte count in patients and controls. Furthermore, we assessed NO production by the Griess method in plasma along with iNOS and NF-κB expression by immunofluorescence method in intestinal tissues of patients and controls. In the same way, we evaluated plasma TNF-α, IL-17A, and IL-10 levels using ELISA. Our results indicate that blood count-based ratios NLR, PLR, and MLR were significantly higher in patients compared to controls. In addition, increased systemic levels of NO, TNF-α, and IL-17A and colonic expression of iNOS and NF-κB were observed in the same patients. Interestingly, the high ratio of NLR and MLR, as well as NO production, was significantly decreased in treated patients. Collectively, our findings suggest that Nitric Oxide, as well as the blood count-based ratios (NLR, PLR, MLR), could constitute useful immuno-markers in complicated Crohn’s Disease, predicting the response to treatment

Keywords: complicated crohn’s disease, nitric oxide, blood count-based ratios, treatments, pro-inflammatory cytokines

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Authors: D. S. Palimkar

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The FRIGDI (functional random integrodifferential inclusion) seems to be new and includes several known random differential inclusions already studied in the literature as special cases have been discussed in the literature for various aspects of the solutions. In this paper, we prove the existence result for FIGDI under the non-convex case of multi-valued function involved in it.Using random fixed point theorem of B. C. Dhage and caratheodory condition. This result is new to the theory of differential inclusion.

Keywords: caratheodory condition, random differential inclusion, random solution, integro-differential inclusion

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Authors: Kohei Inoue, Kenji Hara, Kiichi Urahama

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We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

Keywords: integral images, differential images, differential filters, image fusion

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Authors: Teoman Ozer, Ozlem Orhan

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This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions.

Keywords: λ-symmetry, μ-symmetry, classification, invariant solution

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Authors: Yildiray Keskin, Omer Acan, Murat Akkus

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In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations.

Keywords: fractional diffusion equations, Caputo fractional derivative, reduced differential transform method, partial

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Authors: F. Maass, P. Martin, J. Olivares

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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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Authors: Y. N. Phang, E. F. Loh

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Many researchers have suggested the use of zero inflated Poisson (ZIP) and zero inflated negative binomial (ZINB) models in modeling over-dispersed medical count data with extra variations caused by extra zeros and unobserved heterogeneity. The studies indicate that ZIP and ZINB always provide better fit than using the normal Poisson and negative binomial models in modeling over-dispersed medical count data. In this study, we proposed the use of Zero Inflated Inverse Trinomial (ZIIT), Zero Inflated Poisson Inverse Gaussian (ZIPIG) and zero inflated strict arcsine models in modeling over-dispersed medical count data. These proposed models are not widely used by many researchers especially in the medical field. The results show that these three suggested models can serve as alternative models in modeling over-dispersed medical count data. This is supported by the application of these suggested models to a real life medical data set. Inverse trinomial, Poisson inverse Gaussian, and strict arcsine are discrete distributions with cubic variance function of mean. Therefore, ZIIT, ZIPIG and ZISA are able to accommodate data with excess zeros and very heavy tailed. They are recommended to be used in modeling over-dispersed medical count data when ZIP and ZINB are inadequate.

Keywords: zero inflated, inverse trinomial distribution, Poisson inverse Gaussian distribution, strict arcsine distribution, Pearson’s goodness of fit

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Authors: Lev Idels, Arcady Ponosov

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Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others.

Keywords: delay equations, operator methods, stochastic noise, weak solutions

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Authors: Manas Kotepui, Kwuntida Uthaisar, Phiman Thirarattanasunthon, Bhukdee PhunPhuech, Nuoil Phiwklam

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Introduction: Malaria due to Plasmodium vivax has placed huge burdens on the health, longevity, and general prosperity of large sections of the human population. This study aimed at prospectively collecting information on the clinical profile of Plasmodium vivax from subjects acutely infected with P. vivax residing in some of the highest malaria transmission regions in Thailand. Methods: A retrospective study of malaria cases, hospitalized between 2013 and 2015 was performed. Clinical characteristics, diagnosis, and parasitological results on admission, age, and gender were mined from medical records at Phop Phra Hospital located in endemic areas of Tak Province, Thailand. Venous blood samples were collected at the time of admission to the hospital to determine the present of parasite and also parasite count by thick and thin film examination, and also Complete blood count (CBC) parameters. Results: Results showed that patients infected with Plasmodium vivax (276 cases) had a high monocyte count (mean=390 cells/µL) during initial stage of infection and continuously lower during later stage (any stage with gametocyte, mean=230 cells/µL) of infection (P value=0.021) whereas, patients infected with Plasmodium vivax had a low basophil count (mean=20 cells/µL) during initial stage of infection and continuously higher during later stage of infection (mean at stage with gametocyte=70 cells/µL) (P value=0.033). In addition, patients with more than one stage infection tend to have lower lymphocyte count (mean=1180 cells/µL) than patients with only one stage infection (mean=1350 cells/µL)(P value=0.011) whereas, patients with more than one stage infection tend to have lower basophil count (mean=60 cells/µL) than patients with only one stage infection (mean=80 cells/µL) (P value=0.01). Conclusion: This study indicated that patients infected with Plasmodium vivax had high monocyte count and low basophil count during initial stage of infection which was continuously lower during later stage of infection. Patients with more than one stage infection tend to have lower lymphocyte count than patients with only one stage infection whereas, patients with more than one stage infection tend to have lower basophil count than patients with only one stage infection. This information contributes to better understanding of pathological characteristic of Plasmodium vivax infection.

Keywords: plasmodium vivax, Thailand, asexual erythrocytic stages, hematological parameters

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Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed

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An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.

Keywords: approximant, error estimate, tau method, overdetermination

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Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Lina Wu, Ye Li

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An equivalent relation between a harmonic form and a closed co-closed form is established on a complete non-compact manifold. This equivalence has been generalized for a differential k-form ω from Lq spaces to non-Lq spaces when q=2 in the context of p-balanced growth where p=2. Especially for a simple differential k-form on a complete non-compact manifold, the equivalent relation has been verified with the extended scope of q for from finite q-energy in Lq spaces to infinite q-energy in non-Lq spaces when with 2-balanced growth. Generalized Hadamard Theorem, Cauchy-Schwarz Inequality, and Calculus skills including Integration by Parts as well as Convergent Series have been applied as estimation techniques to evaluate growth rates for a differential form. In particular, energy growth rates as indicated by an appropriate power range in a selected test function lead to a balance between a harmonic differential form and a closed co-closed differential form. Research ideas and computational methods in this paper could provide an innovative way in the study of broadening Lq spaces to non-Lq spaces with a wide variety of infinite energy growth for a differential form.

Keywords: closed forms, co-closed forms, harmonic forms, L^q spaces, p-balanced growth, simple differential k-forms

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial 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. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: Zhan Chen, Wenquan Bi

Abstract:

This paper focuses on examining the strength of Midori against impossible differential attack. The Midori family of light weight block cipher orienting to energy-efficiency is proposed in ASIACRYPT2015. Using a 6-round property, the authors implement an 11-round impossible differential attack on Midori64 by extending two rounds on the top and three rounds on the bottom. There is enough key space to consider pre-whitening keys in this attack. An impossible differential path that minimises the key bits involved is used to reduce computational complexity. Several additional observations such as partial abort technique are used to further reduce data and time complexities. This attack has data complexity of 2 ⁶⁹·² chosen plaintexts, requires 2 ¹⁴·⁵⁸ blocks of memory and 2 ⁹⁴·⁷ 11- round Midori64 encryptions.

Keywords: cryptanalysis, impossible differential, light weight block cipher, Midori

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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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