We give a direct proof of Hahn-Banach and sandwich-type theorems in the setting of convex subinvariant functionals, and a result of separation of convex sets by means of an invariant affine manifold. As consequences and applications, we give some conditions for an optimal solution of minimization problems, proving a Farkas and a Kuhn-Tucker-type theorem.

Mycobacterium ulcerans (MU) has been recognized to be the cause of Buruli ulcer (BU). The association between the ulcer and environmental exposure is identified as a potential factor of spreading BU. The invariant region of the model is determined. In this paper, we explored the power of fractional order in BU SIR model. We applied the Adams-Bashforth predictor corrector method to the proposed model. Numerical simulations are presented to illustrate the benefit of introducing a fractional model.

We present the properties of fuzzy solutions of the nonlocal initial problems for fuzzy differential equations under generalized Hukuhara differentiability (NIP for FIDEs) by the point of view of Hausdorff metric space, for example, existence, uniqueness, boundedness, ... and stability of solutions. The different types of solutions NIP for FDEs are generated by the usage of two different concepts of fuzzy derivative in the formulation of a differential problems. The examples are given to illustrate these results.

In this paper we introduce the concept of proximinality in topological vector spaces. Some results are proved.

In 2002, J. Neggers and H. S. Kim introduced the notion of ß-algebra. The theory of fuzzy sets proposed by L. A. Zadeh in 1965 is generalized in 1986 by K. T. Atanassov an intuitionistic fuzzy sets. The notion of ß -filters was introduced by Henri Cartan in 1937. In 1991, C.S. Hoo introduced the concept of the ß -filters in BCI-algebras and Satyanarayana, et al. [2], introduced interval-valued intuitionistic fuzzy ideals in BF-algebras. In this paper, we define the notion of an Interval-valued intuitionistic L-fuzzy strong ß –filters on ß-algebra and investigate some of their properties.

A 177-point realization of daily exchange rates of the Uganda shilling (UGX) – Nigerian naira (NGN) from 22nd September, 2015 to 16th March, 2016, is analyzed by Box-Jenkins methods. The original series being non-stationary is differenced seasonally i.e. on a seven-day basis. A further non-seasonal differencing is done to ensure seasonality. These differences of the seasonal differences of the series are modeled by seasonal autoregressive integrated moving average (SARIMA) approach. The first 170 values are used for the modeling process and the remaining 7 are used for out-of-sample forecast goodness-of-fit test. By a new fitting algorithm, it is concluded that the time series follows the additive SARIMA (1,1,0)x(1,1,0)7 model. Forecasts obtained for the daily rates from March 10 to March 16, 2016 agree so closely with the observed values that the calculated goodness-of-fit chi-square test statistic is far from being statistically significant with a p-value of more than 99%. Daily exchange rates between the two currencies may be simulated or forecasted by the model.

This paper is an extension of the work done in [S. Pamuk, Qualitative Analysis of a Mathematical Model for Capillary Formation in Tumor Angiogenesis, Math. Models Methods Appl. Sci. 13 (1) (2003) 19-33] to a further 2D-mathematical analysis of a model for tumor angiogenesis in the absence of endothelial cell proliferation term. We actually obtain the long time dynamics of endothelial cells in the extra cellular matrix under some assumptions and using the results of a 1D-mathematical analysis. Also, the stability of the steady-state solution is studied. Some figures obtained from the numerical results are presented.

Longitudinal data differs from other types of data as we take more than one observation from every subject at different occasion or under different conditions. The response variable may be continuous, categorical or count. In this article the focus is on count response. The Poisson distribution is the most suitable discrete distribution for count data. Missing values are not uncommon in longitudinal data setting. Possibility of having missing data makes all traditional methods give biased and inconsistent estimates. The missing data mechanism is missing completely at random (MCAR), missing at random (MAR), or missing not at random (MNAR). This article compares different methods of analysis for longitudinal count data in the presence of missing values. The aim is to compare the efficiency of these methods. The relative bias and relative efficiency is used as criteria of comparison. Simulation studies are used to compare different methods. This is done under different settings such as different sample sizes and different rates of missingness. Also, the methods are applied to a real data.

In this paper, we determine the Laplacian spectra of graphs obtained by appending end vertex to all vertices of a defined class of graphs called the base graph. The end vertices allow for a quick solution to the eigen-vector equations of the Laplacian matrix satisfying the characteristic equation, and the solutions to the eigenvalues of the Laplacian matrix of the base graph arise. We determine the relationship between the eigenvalues of the Laplacian matrix of the base graph and the eigenvalues of the Laplacian matrix of the new graph as constructed above, and determine that if is an eigenvalue of the Laplacian matrix of the base graph, then is an eigenvalue of the Laplacian matrix of the constructed graph. We then determine the Laplacian spectra for such graphs where the base graph is one of the well-known classes of graphs, namely the complete, complete split-bipartite, cycle, path, wheel and star graphs. We then use the Laplacian spectra to determine the Laplacian energy of the graph, constructed from the base graphs, for each of the above classes of graphs. We then analyse the case where only one end vertex is appended to each vertex in the base graph, and determine the Laplacian energy for large values of , the total number of vertices in the constructed graph.In the last section, we investigate the eigen-bi-balance of the graphs using the eigenvalues of the Laplacian matrix for graphs with appended end vertices, and consider the example of the star sun graph

In this paper, we determine the Laplacian spectra of graphs obtained by appending end vertex to all vertices of a defined class of graphs called the base graph. The end vertices allow for a quick solution to the eigen-vector equations of the Laplacian matrix satisfying the characteristic equation, and the solutions to the eigenvalues of the Laplacian matrix of the base graph arise. We determine the relationship between the eigenvalues of the Laplacian matrix of the base graph and the eigenvalues of the Laplacian matrix of the new graph as constructed above, and determine that if is an eigenvalue of the Laplacian matrix of the base graph, then is an eigenvalue of the Laplacian matrix of the constructed graph. We then determine the Laplacian spectra for such graphs where the base graph is one of the well-known classes of graphs, namely the complete, complete split-bipartite, cycle, path, wheel and star graphs. We then use the Laplacian spectra to determine the Laplacian energy of the graph, constructed from the base graphs, for each of the above classes of graphs. We then analyse the case where only one end vertex is appended to each vertex in the base graph, and determine the Laplacian energy for large values of , the total number of vertices in the constructed graph.In the last section, we investigate the eigen-bi-balance of the graphs using the eigenvalues of the Laplacian matrix for graphs with appended end vertices, and consider the example of the star sun graph

Nigeria belongs to the group of Next Eleven (N-11), which is a group of 11 countries identified by the investment bank Goldman Sachs in 2007 as having high potential of becoming the world’s largest economies in the 21st century. There is a need to determine how it can attain economic growth while conserving energy and reducing emission. This paper looks at the relationship between GDP and CO2 emission in the light of the Environmental Kuznet Curve (EKC). The method of least square polynomials was employed. The results obtained aligned with the EKC hypothesis.

The study presents a deterministic model for radicalization process in Kenya and use the model to assess impact of rehabilitation centers to radicalization burden. The possibility of other drivers of radicalization to individuals who are not religious fanatics, and also individuals in rehabilitated subclass continuing being violent was considered. The model incorporated rehabilitation of the radicalized but peaceful individuals in subclass R (t), and also radicalized but violent individuals in subclass T (t), allowing recovery of individuals in subclass R (t) from the intervention of good clergies. The stationary points were computed, their stabilities investigated and important thresholds determining the progression of the radicalization evaluated. The model sensitivity indices indicate that high intervention rates hold great promise to reduce the radicalization burden.

In this paper, we constructed a control operator sequel to an earlier constructed control operator in one of our papers which enables an Extended Conjugate Gradient Method (ECGM) to be employed in solving discrete time linear quadratic regulator problems with delay parameter in the state variable. The construction of the control operator places scalar linear delay problems of the type within the class of problems that can be solved with the ECGM and it is aimed at reducing the rigours faced in using the classical methods in solving this of class of problem. More so, the authors of this paper desire that the application of this control operator will further improve the results of the ECGM as well as increasing the variant approaches used in solving the said class of optimal control problem.

Most time series assume both linear and non linear components because of their random nature. Thus, the classical linear models are not appropriate for modeling series with such behaviour. This work was motivated by the need to propose a vector moving average (MA) bilinear concept that caters for the linear and non linear components of a series on the basis of the ‘orders’ of the linear MA process. To achieve this, a matrix that preserved the ‘orders’ of the linear processes was formulated with given conditions. With the introduction of diagonal matrix of lagged white noise processes, some special bilinear models emerged and the ‘orders’ of the pure linear MA processes were maintained in both the linear and non linear parts. The derived vector bilinear models were applied to revenue series, and the result showed that the models gave a good fit which depicted its validity.

We propose a general methodology allowing modeling the natural phenomena mathematically. After having to clarify the concepts and to propose a classi?cation of the models according to their functions of description, prediction and comprehension, we give a de?nition of the mathematical model which integrates prediction and comprehension. Thereafter, we propose with details the great stages of mathematical modeling. An application of methodology suggested is made in a general way in epidemiology. Finally we proceed in example to the modeling and mathematical analyis of in?uenza epidemic in a heterogeneous environment taking account the mobility of the individuals.

It is investigated the spectral properties of some operator, rationally depending on parameter in Hilbert space. It is known that the problem of oscillations of viscous liquid located in a stationary vessel and having a free surface, leads to the investigation of such type operator equations. Methods of investigations in this work are the methods of functional analysis, spectral theory of operators, theory of functions and multiparameter system of operators. It is famous that the notions of completeness of eigen and associated (e.a.) vectors, multiple completeness of them, question of existence of bases of e.a. vectors, multiple bases, asymptotic of eigenvalues are the fundamental directions in spectral theory of operators in Hilbert space. In this paper the authors are proved the possibility of existence of two bases of e.a. vectors of considerable equation in the Hilbert space, proved the existence of two sequences of eigenvalues of operator equation and the asymptotic of corresponding eigenvalues.

The aim of this study is to examine the characteristics of the tropospheric Nitrogen Dioxide (NO2) concentrations over the five states of South Eastern Nigeria retrieved from Ozone Monitoring Instrument (OMI) data from 2010 – 2015. The mean concentration ranges from molecules/cm2 in Abakaliki (with the least commercial, industrial and vehicle activities) to in Aba, the industrial and commercial centre with coefficients of variation of 17.7% and 15.8% respectively. Results using non-parametric Mann-Kendall (MK) tests show a significant (p < 0.05) increasing levels of NO2 columns in the region. For each of the seven studied cities, there is a significant seasonal cycle of NO2 columns. NO2 maximum was observed in dry (harmattan) season (December – March) and minimum in wet (rainy) season (May, June, October). On the average, the annual change rate for the entire Southeast was 1.72% while the 5% uncertainty interval for the region was , which indicates a highly polluted region.

The aim of this paper is to investigate and give a closed form solution to an investment and consumption decision problem where the risk-free asset has a rate of return that is driven by the Ornstein-Uhlenbeck Stochastic interest rate of return model. The maximum principle is applied to obtain the HJB equation for the value function. Owing to the introduction of the consumption factor and the Ornstein-Uhlenbeck Stochastic interest rate of return, the HJB equation derived becomes much more difficult to deal with than the one obtained in literature. In the same spirit with the techniques literature, the nonlinear second-order partial differential equation was transformed into an ordinary differential equation; specifically, the Bernoulli equation, using elimination of dependency on variables for easy tackling.

This paper proposes a self-starting block hybrid method of order for the solution of general second order ODEs of the form , with associated initial or boundary conditions. Derivation of the continuous hybrid formulation was based on the use of hermite polynomial as basis function. The continuous hybrid formulation enables us to evaluate and then differentiate at some grid and off-grid points to obtained discrete schemes which were used in block form. This approach eliminates the need for starting values. The computational burden and computer time wastage involved in the usual reduction of the second order problem into system of first order equations are avoided by this procedure. The stability properties of our method reveal that the method is consistent and zero stable, hence convergent. Numerical results suggest that the method performs favorably with the existing methods.

In this paper, we determine the spectra of graphs obtained by appending h end vertex to all vertices of a defined class of graphs called the base graph. The end vertices allow for a quick solution to the eigen-vector equations satisfying the characteristic equation, and the solutions to the eigenvalues of the base graph arise. We determine the relationship between the eigenvalues of the base graph and the eigenvalues of the new graph as constructed above, and determine that if a is an eigenvalue of the base .........

In this paper, we introduce the notions of vague weak LI - ideals and normal vague LI - ideals of lattice implication algebras. We discuss some properties of vague weak LI - ideals and normal vague LI - ideals. We prove that every VLI - ideal extended to normal vague LI - ideal. We study the relations between vague weak LI - ideals and VLI - ideals, vague weak LI - ideals and VILI - ideals, vague weak LI - ideals and vague weak filters, normal vague LI - ideals and vague maximal LI - ideals.

A felicitous labeling of a graph G, with q edges is an injection f : V(G) ? {0, 1, 2,. . . , q} so that the induced edge labels f *(xy) = (f(x) + f(y)) (mod q) are distinct.

This work has been presented at ICFAS2016, ”International Congress on Fundamental and Applied Sciences, 22-26 Aug, 2016, Istanbul, Turkey”. In this paper we present a 2D mathematical model which is related to the interaction between tumor cell and its inhibitor. We obtain some necessary conditions in order for Turing instability to occur. We also provide some numerical examples to verify our theoretical results.