maximizing the least signless laplacian eigenvalue of unicyclic graphs abstract in this paper a graph with the maximum least signless laplacian eigenvalue among all connected unicyclic graphs with fixed order is determined

fermat reyes method in the ring of fermat reals abstract to discover derivatives pierre de fermat used to assume a non zero increment h in the incremental ratio and after some calculations to set h 0 in the final result this method which sounds as inconsistent can be perfectly formalized with the fermat reyes theorem about existence and uniqueness of a smooth incremental ratio in the present work we will introduce the cartesian closed category where to study and prove this theorem and describe in general the fermat method the framework is the theory of fermat reals an extension of the real field containing nilpotent infinitesimals which does not need any knowledge of mathematical logic this key theorem will be essential in the development of differential and integral calculus for smooth functions defined on the ring of fermat reals and also for infinite dimensional operators like derivatives and integrals

the smallest eigenvalue of the signless laplacian recently the signless laplacian matrix of graphs has been intensively investigated while there are many results about the largest eigenvalue of the signless laplacian the properties of its smallest eigenvalue are less well studied the present paper surveys the known results and presents some new ones about the smallest eigenvalue of the signless laplacian

inferring operating rules for reservoir operations using fuzzy regression and anfis the methods of ordinary least squares regression olsr fuzzy regression fr and adaptive network based fuzzy inference system anfis are compared in inferring operating rules for a reservoir operations optimization problem dynamic programming dp is used as an example optimization tool to provide the input output data set to be used by olsr fr and anfis models the coefficients of an fr model are found by solving a linear programming lp problem the objective function of the lp is to minimize the total fuzziness of the fr model which is related to the width of fuzzy coefficients in the regression model before applying fr to the reservoir operations problem two fr formulations and interval regression ir are first examined in a simple tutorial example anfis is also used to derive the reservoir operating rules as fuzzy if then rules the olsr fr and anfis based rules are then simulated and compared based on their performance in simulation the methods are applied to a long term planning problem as well as to a medium term implicit stochastic optimization model the results indicate that fr is useful to derive operating rules for a long term planning model where imperfect and partial information is available anfis is beneficial in medium term implicit stochastic optimization as it is able to extract important features of the system from the generated input output set and represent those features as general operating rules

new topologies on colombeau generalized numbers and the fermat reyes theorem abstract based on the theory of fermat reals we introduce new topologies on spaces of colombeau generalized points and derive some of their fundamental properties in particular we obtain metric topologies on the space of near standard generalized points that induce the standard euclidean topology on the reals we analyze the description of the sharp topology in terms of the natural extension of the absolute value or of the defining semi norms in the case of locally convex spaces thereby preserving a number of classical notions building on a new point value characterization of colombeau generalized functions we prove a fermat reyes theorem that forms the basis of an approach to differentiation on spaces of generalized functions close to the classical one

the ring of fermat reals abstract we give the definition of the ring of fermat reals a simple extension of the real field containing nilpotent infinitesimals the construction takes inspiration from smooth infinitesimal analysis but provides a powerful theory of actual infinitesimals without any need of a background in mathematical logic in particular it is consistent with classical logic we face the problem to decide if the product of powers of nilpotent infinitesimals is zero or not the identity principle for polynomials the characterization of invertible elements and some applications to taylor s formulas

signless laplacians of finite graphs we survey properties of spectra of signless laplacians of graphs and discuss possibilities for developing a spectral theory of graphs based on this matrix for regular graphs the whole existing theory of spectra of the adjacency matrix and of the laplacian matrix transfers directly to the signless laplacian and so we consider arbitrary graphs with special emphasis on the non regular case the results which we survey old and new are of two types a results obtained by applying to the signless laplacian the same reasoning as for corresponding results concerning the adjacency matrix b results obtained indirectly via line graphs among other things we present eigenvalue bounds for several graph invariants an interpretation of the coefficients of the characteristic polynomial a theorem on powers of the signless laplacian and some remarks on star complements

constrained state formulation for the stochastic control of multireservoir systems a new formulation is presented for the analysis of multireservoir systems based on the development of first and second moment expressions for the stochastic storage state variables these expressions give explicit consideration to the maximum and minimum storage bounds in the reservoir system a feature not incorporated in some existing formulations based on traditional control theory using this analysis expected values of the storage states variances of storage release policies reliability levels and failure probabilities useful information in the context of reservoir operations and design can be obtained from a nonlinear programming solution the approach does not involve any discretization of the system variables the results for the means and standard deviations of the storage states for a multireservoir system compare favorably with those obtained from simulation

signless laplacian spectral radii of graphs with given chromatic number abstract let g be a simple graph with vertices v 1 v 2 v n of degrees d 1 d 2 d n respectively let a be the 0 1 adjacency matrix of g and d be the diagonal matrix diag d 1 d 2 d n q g d a is called the signless laplacian of g the largest eigenvalue of q g is called the signless laplacian spectral radius or q spectral radius of g denote by g the chromatic number for a graph g in this paper for graphs with order n the extremal graphs with both the given chromatic number and the maximal q spectral radius are characterized the extremal graphs with both the given chromatic number 4 5 6 7 and the minimal q spectral radius are characterized as well

the least eigenvalue of signless laplacian of graphs under perturbation abstract we investigate how the least eigenvalue of the signless laplacian of a graph changes by relocating a bipartite branch from one vertex to another vertex and minimize the least eigenvalue of the signless laplacian among the class of connected graphs with fixed order which contains a given non bipartite graph as an induced subgraph

calculus in the ring of fermat reals part i integral calculus abstract we develop integral calculus for quasi standard smooth functions defined on the ring of fermat reals the approach is by proving the existence and uniqueness of primitives besides the classical integral formulas we show the flexibility of the cartesian closed framework of fermat spaces to deal with infinite dimensional integral operators the total order relation between scalars permits to prove several classical order properties of these integrals and to study multiple integrals on peano jordan like integration domains

the least signless laplacian eigenvalue of non bipartite graphs with given stability number abstract in this paper we investigate the least eigenvalue of signless laplacian matrix of a connected graph and determine the graphs which have the minimum least signless laplacian eigenvalue among all nonbipartite graphs with given stability number n 1 2 or covering number 2 n 1 2 respectively

first eigenvalue of nonsingular mixed graphs with given number of pendant vertices abstract let g be a mixed graph and l g be the laplacian matrix of the mixed graph g the first eigenvalue of g is referred to the least nonzero eigenvalue of l g let mg n k be the set of nonsingular mixed graphs with n vertices and k pendant vertices where n 4 in this paper up to a signature matrix we determine the unique graph with the minimal first eigenvalue among all graphs in m g n k thus we obtain a lower bound for the first eigenvalue of a mixed graph in terms of the number of pendant vertices

the domination number and the least q eigenvalue abstract in this paper for a nonbipartite graph with both order n and domination number we show that it contains a nonbipartite unicyclic spanning subgraph with the same domination number we also present some results about the changing of the domination number when the structure of a graph is changed by investigating the relation between the domination number and the least q eigenvalue of a graph we minimize the least q eigenvalue among all the nonbipartite graphs with both order n 4 and given domination number n 1 3

minimizing the least eigenvalues of unicyclic graphs with application to spectral spread the spread of a graph is defined to be the difference between the largest eigenvalue and the least eigenvalue of the adjacency matrix of the graph let u k denote the set of connected unicyclic graphs of order n and girth k and let un denote the set of connected unicyclic graphs of order n in this paper we determine the unique graph with minimum least eigenvalue respectively the unique graph with maximum spread among all graphs in u k we finally characterize the unique graph with minimum least eigenvalue respectively the unique graph with maximum spread among all graphs in un

a sharp lower bound for the least eigenvalue of the signless laplacian of a non bipartite graph we prove that the minimum value of the least eigenvalue of the signless laplacian of a connected non bipartite graph with a prescribed number of vertices is attained solely in the unicyclic graph obtained from a triangle by attaching a path at one of its endvertices

on the least q eigenvalue of a non bipartite hamiltonian graph abstract in this paper we study the least q eigenvalue of a non bipartite hamiltonian graph and determine all non bipartite hamiltonian graphs whose least q eigenvalue attains the minimum among all non bipartite hamiltonian graphs on n vertices

unoriented laplacian maximizing graphs are degree maximal abstract a connected graph is said to be unoriented laplacian maximizing if the spectral radius of its unoriented laplacian matrix attains the maximum among all connected graphs with the same number of vertices and the same number of edges a graph is said to be threshold maximal if its degree sequence is not majorized by the degree sequence of any other graph and in addition the graph is connected it is proved that an unoriented laplacian maximizing graph is maximal and also that there are precisely two unoriented laplacian maximizing graphs of a given order and with nullity 3 our treatment depends on the following known characterization a graph g is threshold maximal if and only if for every pair of vertices u v of g the sets n u v n v u where n u denotes the neighbor set of u in g are comparable with respect to the inclusion relation and in addition the graph is connected a conjecture about graphs that maximize the unoriented laplacian matrix among all graphs with the same number of vertices and the same number of edges is also posed

minimizing variance of reservoir systems operations benefits using soft computing tools soft computing based tools including fuzzy inference systems fis artificial neural networks ann and genetic algorithms ga are used here to tackle the minimization of variance of benefits from reservoir operation variance reduction is a very hard optimization problem and solvable only using implicit methods like simulation especially if the problem is nonlinear first a recently developed stochastic optimization method develops the optimal release policy which is simply the recommended release in each season of the system whose objective function maximizes the expected benefits the policy is then simulated for a long inflow series to provide the trajectories of optimal releases and storages of the reservoir these trajectories are then used as input output data to train an adaptive neuro fuzzy inference system anfis to obtain updated fuzzy operating rules the anfis based fuzzy rules are simulated and compared with policies developed using a multiple regression analysis a commonly used method in water resources optimization as the anfis performed better further a parameterized t norm operator is applied and its parameters numbering only two are optimized through ga but with the objective of variance reduction in the benefits achieved results compare the better performance of the anfis based policies with other methods such as stochastic dynamic programming and the original stochastic method to demonstrate the usefulness of ga optimized parameters of a t norm fuzzy operator for variance reduction

the least q eigenvalue with fixed domination number abstract denote by lg l the lollipop graph obtained by attaching a pendant path p v g v g 1 v g l l 1 to a cycle c v 1 v 2 v g v 1 g 3 a f g l g r a p h of order n g 1 is defined to be the graph obtained by attaching n g l pendent vertices to some of the nonpendant vertices of lg l in which each vertex other than v g l 1 is attached at most one pendant vertex a f g l graph is a f g l g r a p h in which vg is attached with pendant vertex denote by qmin the least q e i g e n v a l u e of a graph in this paper we proceed on considering the domination number the least q eigenvalue of a graph as well as their relation further results obtained are as follows i some results about the changing of the domination number under the structural perturbation of a graph are represented ii among all nonbipartite unicyclic graphs of order n with both domination number and girth g g n 1 the minimum qmin attains at a f g l graph for some l iii among the nonbipartite graphs of order n and with given domination number which contain a f g l graph as a subgraph some lower bounds for qmin are represented iv among the nonbipartite graphs of order n and with given domination number n 2

signless laplacian spectral radius and hamiltonicity we give tight conditions on the signless laplacian spectral radius of a graph for the existence of hamiltonian paths and cycles

extremizing first eigenvalue of 3 colored digraphs made with given blocks abstract this article describes the structure of the non singular connected 3 colored digraphs extremizing the first eigenvalue among all such graphs made with some given blocks as an application we determine the non singular unicyclic 3 colored digraph which minimizes the first eigenvalue over all such graphs with fixed order and girth