lifespan of solutions to semilinear damping wave equations in de sitter spacetime abstract this paper studies blowup phenomena for two kind of initial value problem of semilinear damping wave equations in de sitter spacetime the first problem comes from the latter problem of conjecture of strauss in de sitter spacetime and the second problem arises from the latter problem of conjecture of glassey in de sitter spacetime we give blowup and lifespan of solutions on those two problems comparing with non damping case established in yan 2018 one can see that the damping term with a positive bounded time dependent coefficient does not effect blowup of solutions meanwhile we establish a new ode blowup result concerning damping term

lifespan of semilinear wave equation with scale invariant dissipation and mass and sub strauss power nonlinearity abstract in this paper we study the blow up of solutions for semilinear wave equations with scale invariant dissipation and mass in the case in which the model is somehow wave like a strauss type critical exponent is determined as the upper bound for the exponent in the nonlinearity in the main theorems two blow up results are obtained for the subcritical case and for the critical case respectively in both cases an upper bound lifespan estimate is given

construction of a multisoliton blowup solution to the semilinear wave equation in one space dimension we consider the semilinear wave equation with power nonlinearity in one space dimension given a blow up solution with a characteristic point we refine the blow up behavior first derived by merle and zaag we also refine the geometry of the blow up set near a charac teristic point and show that except may be for one exceptional situation it is never symmetric with the respect to the characteristic point then we show that all blow up modalities predicted by those authors do occur more precisely given any integer k 2 and 0 we construct a blow up solution with a characteristic point a such that the asymptotic behavior of the solution near a t a shows a decoupled sum of k solitons with alternate signs whose centers in the hyperbolic geometry have 0 as a center of mass for all times

computation of the bit error rate of coherent m ary psk with gray code bit mapping efficient computation of the bit error rate ber for the coherent m ary psk signals with gray code bit mapping is considered a closed form expression for the exact ber of 8 ary psk is presented tight upper and lower bounds on ber are also obtained for m ary psk with larger m

on the profile of energy concentration at blow up points for subconformal focusing nonlinear waves we consider singularities of the focusing subconformal nonlinear wave equation and some generalizations of it at noncharacteristic points on the singularity surface merle and zaag have identified the rate of blow up of the h1 norm of the solution inside cones that terminate at the singularity we derive bounds that restrict how this h1 energy can be distributed inside such cones our proof relies on new localized estimates obtained using carlemantype inequalities for such nonlinear waves these bound the lp 1 norm in the interior of timelike cones by their h1 norm near the boundary of the cones such estimates can also be applied to obtain certain integrated decay estimates for globally regular solutions to such equations in the interior of time cones

aggregation operators ordering and bounds standard ordering of aggregation operators in several distinguished classes is characterized lower and upper bounds of finite systems in those classes of aggregation operators are discussed several examples are given

openness of the set of non characteristic points and regularity of the blow up curve for the 1 d semilinear wave equation we consider here the 1 d semilinear wave equation with a power nonlinearity and with no restriction on initial data we first prove a liouville theorem for that equation then we consider a blow up solution its blow up curve x mapsto t x and i 0 subset mathbb r the set of non characteristic points we show that i0 is open and that t x is c1 on i0 all these results fundamentally use our previous result in 19 showing the convergence in selfsimilar variables for x in i 0

on the existence and nonexistence of global solutions for certain semilinear exterior problems with nontrivial robin boundary conditions abstract we consider three types of semilinear equations elliptic parabolic and hyperbolic posed in the n dimensional exterior domain r n d where n 2 and d is the closed unit ball in r n a nontrivial robin boundary condition is imposed on the boundary of d using a test function approach with judicious choices of the test functions we show that the considered problems share a common critical behavior we discuss separately the cases n 2 and n 3 moreover in the case n 3 the dependence of the critical exponent on initial data is discussed to the best our knowledge the study of the critical behavior in an exterior domain with a nontrivial robin boundary condition has never been studied in the literature

wave equations with concentrated nonlinearities in this paper we address the problem of wave dynamics in the presence of concentrated nonlinearities given a vector field v on an open subset of and a discrete set with n elements we define a nonlinear operator v y on which coincides with the free laplacian when restricted to regular functions vanishing at y and which reduces to the usual laplacian with point interactions placed at y when v is linear and represented by a hermitian matrix we then consider the nonlinear wave equation and study the corresponding cauchy problem giving an existence and uniqueness result when v is lipschitz the solution of such a problem is explicitly expressed in terms of the solutions of two cauchy problems one relative to a free wave equation and the other relative to an inhomogeneous ordinary differential equation with delay and principal part the main properties of the solution are given and when y is a singleton the mechanism and details of blow up are studied

precise error rate analysis of bandwidth efficient bpsk in nakagami fading and cochannel interference the bit error rate ber of bandlimited binary phase shift keying in a fading and cochannel interference cci environment is derived for the case of perfect coherent detection the fading and interference model assumed is general and of interest for microcellular system studies the model allows both desired signal and interfering signals to experience arbitrary amounts of fading severity a precise ber expression is derived using a characteristic function method using this accurate analytical result the impact of the interfering users fading severity on the desired user error rate is examined the bers obtained under perfect coherent detection are also valid as lower performance bounds for practical realizable receivers where ideal coherent detection is difficult to implement the error rate performance of a novel bandwidth efficient pulse shape is determined for the general fading and cci environment analysis and numerical results show that the new pulse can provide better ber performance than the widely used raised cosine pulse

solutions blowing up on any given compact set for the energy subcritical wave equation abstract we consider the focusing energy subcritical nonlinear wave equation t t u u u p 1 u in r n n 1 given any compact set k r n we construct finite energy solutions which blow up at t 0 exactly on k the construction is based on an appropriate ansatz the initial ansatz is simply u 0 t x t a x 2 p 1 where a 0 vanishes exactly on k which is a solution of the ode h h p we refine this first ansatz inductively using only ode techniques and taking advantage of the fact that for suitably chosen a space derivatives are negligible with respect to time derivatives we complete the proof by an energy argument and a compactness method

on the computation for blow up solutions of the nonlinear wave equation we consider in this paper the 1 dim nonlinear wave equation frac partial 2 u partial t 2 t x frac partial 2 u partial x 2 t x u 1 alpha t x alpha 0 and its finite difference analogue it is known that the solution of the current equation may become unbounded in finite time a phenomenon which is known as blow up moreover since the nonlinear wave equation enjoys finite speed of propagation even if the solution has become unbounded at certain points the solution continues to exist blows up at later times and forms the so called blow up curve up to the present however numerical approximation for blow up problems gave only the convergence up to the blow up time of vert u t cdot vert infty in fact adaptive time mesh strategy was used to numerically reproduce the phenomenon of finite time blow up nevertheless computation using such schemes can not be extended beyond the blow up time of vert u t cdot vert infty this is a fatal problem when computing blow up solutions for the nonlinear wave equation as a consequence we reconsider a finite difference scheme whose temporal grid size is given uniformly and propose an algorithm with rigorous convergence analysis to numerically reconstruct the blow up curve for the nonlinear wave equation

differentiability of the blow up curve for one dimensional nonlinear wave equations consider the cauchy problem rac artial 2 u artial t 2 umimits i 1 n rac artial 2 u artial x i 2 f u x n athbb r n t 0 ueft x 0 ight feft x ight eft x n athbb r n ight u t eft x 0 ight geft x ight eft x n athbb r n ight with n 3 it is well known that if f u is superlinear i e feft u ight a eft u ight p ifeft u ight o nfty eft a 0 p 1 ight 0 1 then solutions generally blow up in finite time see 2 6

a discrete phenomenon in the c and analytic regularity of the blow up curve of solutions to the liouville equation in one space dimension we give a complete discussion of the c or analytic regularity of blow up curves for cauchy problems or some mixed problems for the liouville equation in one space dimension in the case of mixed problems the regularity results depend on the boundary condition actually we show the existence of a sequence of boundary conditions for which the regularity of the blow up curve is better than in the general case

an orness measure for quasi arithmetic means in this paper an orness measure to reflect the or like degree of the quasi arithmetic mean operator is proposed with the generating function representation method some properties of a quasi arithmetic mean associated with its orness measure are analyzed then the paper focuses on two kinds of parameterized quasi arithmetic means with exponential function and power function generators respectively some properties of them are examined and compared as the aggregation value for any set always monotonically increases with the orness level the orness level can be used as a control parameter to represent the decision maker s preference a generic method to get the quasi arithmetic mean operator which makes the aggregation result consistent with its orness level is also examined finally the properties of the quasi arithmetic mean and that of the exponential and power function generators are extended to the weighted quasi arithmetic mean by considering the importance of the aggregated elements

global nonexistence results for a class of hyperbolic systems abstract our concern in this paper is to prove blow up results to the non autonomous nonlinear system of wave equations u t t u a t x v p v t t v b t x u q t 0 x r n in any space dimension we show that a curve f p q 0 depending on the space dimension on the exponents p q and on the behavior of the functions a t x and b t x exists such that all nontrivial solutions to the above system blow up in a finite time whenever f p q 0 our method of proof uses some estimates developed by galaktionov and pohozaev in 11 for a single non autonomous wave equation enabling us to obtain a system of ordinary differential inequalities from which the desired result is derived our result generalizes some important results such as the ones in del santo et al 1996 12 and galaktionov and pohozaev 2003 11 the advantage here is that our result applies to a wide variety of problems

the blow up boundary for nonlinear wave equations consider the cauchy problem for a nonlinear wave equation du f u in n space dimensions n x with x continuously difierentiable introduction consider the nonlinear wave equation 0 1 uu u t au f u for x 6 r i 0 with the initial data 0 2 u x 0 x ul x 0 g x for x g rn it is well known that if f u is nonnegative and superlinear then in general a solution cannot exist for all times furthermore if t is the supremum of all times s such that a classical solution exists for all 0 t s then sup w jc t oo if t t

finite time blow up to critical semilinear wave equation outside the ball in 3 d abstract in this paper we study the initial boundary value problem of critical semilinear wave equation with small initial data in 3 d blow up result will be established no matter how small the data are we find a radial and positive solution of the corresponding linear problem then our blow up result follows from the idea of zhou and han 2014 what is more we get the upper bound of the lifespan estimate

existence and classification of characteristic points at blow up for a semilinear wave equation in one space dimension we consider the semilinear wave equation with power nonlinearity in one space dimension we first show the existence of a blow up solution with a characteristic point then we consider an arbitrary blow up solution u x t the graph x mapsto t x of its blow up points and scr s subset bbb r the set of all characteristic points and show that scr s has an empty interior finally given x 0 in scr s we show that in selfsimilar variables the solution decomposes into a decoupled sum of at least two solitons with alternate signs and that t x forms a corner of angle pi over 2 at x 0

continuous archimedean t norms and their bounds upper and lower bounds in the class of continuous archimedean t norms are studied the existence of strict nilpotent bounds of finite families of strict nilpotent t norms is shown in a constructive way based on the additive generators of the corresponding t norms in general a nilpotent lower bound and a strict upper bound of a finite system of any continuous archimedean t norms can be found some examples and some applications are given by the duality similar results for bounds of continuous archimedean t conorms can be derived

the error performance of gray encoded qpsk and 8 psk schemes in a fading channel with cochannel interference closed form ber bit error rate expressions are derived for gray encoded qpsk quadrature phase shift keying and 8 psk schemes using coherent detection in a slow rayleigh fading narrowband channel with fading cochannel interference earlier work has been limited to deriving the approximate ber using the canonical stein 1961 receiver concept the symbol error rate ser for the qpsk scheme is also derived the desired signal and the cochannel interferer are both psk signals modulated by different baseband pulses with identical signaling rate

blow up theorem for semilinear wave equations with non zero initial position abstract one of the features of solutions of semilinear wave equations can be found in blow up results for non compactly supported data in spite of finite propagation speed of the linear wave we have no global in time solution for any power nonlinearity if the spatial decay of the initial data is weak this was first observed by asakura 1986 2 finding out a critical decay to ensure the global existence of the solution but the blow up result is available only for zero initial position having positive speed in this paper the blow up theorem for non zero initial position by uesaka 2009 22 is extended to higher dimensional case and the assumption on the nonlinear term is relaxed to include an example u p 1 u moreover the critical decay of the initial position is clarified by example

parameterized defuzzification with continuous weighted quasi arithmetic means an extension parameterized aggregation becomes an attractive idea in many applications by applying the quasi arithmetic mean based defuzzification method and its orness measure we extend the properties of discrete quasi arithmetic mean with an orness measure to the case of continuous weighted quasi arithmetic means and apply them to the parameterized estimation of fuzzy or random variables when facing the uncertainty of these variables the decision maker can obtain the crisp value estimation which is always consistent with his her preference information two families of continuous weighted quasi arithmetic means with exponential and power function generators are discussed combining these conclusions with that of the discrete case we can understand better the properties of quasi arithmetic means and extend their possible applications

the blow up surface for nonlinear wave equations with small spatial velocity on considere le probleme de cauchy pour u tt e 2 u f u a d dimensions d espace 3 ou f u est superlineaire et non negative la solution explose sur une surface t e x on note par t x la surface d explosion correspondant a v f v on demontre que e x x ce 2 e x x ce 2 dans un voisinage d un point x 0 ou x 0

a nonlinear nonlocal wave equation arising in combustion theory the initial value problem for the equation 2 t2 2 x2 t t 2 t 2 x2 et 1 is considered it is proved that under some restrictions on the initial data there is a curve denoted by t x which is positive lipschitz continuous and satisfies x 0 the case of 1 is also studied the solution for 1 blows up on t x and it is proved that under certain conditions the solutions for 1 converge to the one for 1 as 1 and lim inf 1 x x

blow up of the su 2 c yang mills fields it is remarked that if the gauge group is not compact finite time blowing up yang mills fields over the minkowski spaces may exist the example taken is g su 2 c it is shown that blow up can occur in an arbitrarily small time interval when the initial data of the fields are suitably chosen

evolution in time of l fuzzy context sequences in this work we consider a complete lattice l and we study l fuzzy context sequences which represent the evolution in time of an l fuzzy context to carry out this study in the first part of the paper we consider n ary owa operators in complete lattices which enable us to make a general analysis and a temporal analysis at any moment in time of l fuzzy context sequences after that evolution in time of the relationship between the objects and the attributes is considered in particular we analyze the concepts of trend and persistent formal contexts finally we illustrate our results with an example where we consider the particular lattice l j 0 1

a characterization of the ordering of continuous t norms abstract given two t norms t 1 and t 2 it is quite often difficult or even impossible to check directly whether t 1 t 2 in schweizer and sklar 1983 a necessary and sufficient condition is given for continuous archimedean t norms to be comparable we simplify this result proving a sufficient condition which involves only one argument of a one place function rather than two arguments this result is applied to show the monotonicity of some well known classes of t norms next we generalize the result of schweizer and sklar to the case of all continuous t norms and present also a sufficient condition which is again easier to check

determination of the curvature of the blow up set and refined singular behavior for a semilinear heat equation we consider u x t a solution of ut u u p 1u which blows up at some time t 0 where u rn 0 t r p 1 and n 2 p n 2 under a nondegeneracy condition we show that the mere hypothesis that the blow up set s is continuous and n 1 dimensional implies that it is c2 in particular we compute the n 1 principal curvatures and directions of s moreover a much more refined blow up behavior is derived for the solution in terms of the newly exhibited geometric objects refined regularity for s and refined singular behavior of u near s are linked through a new mechanism of algebraic cancellations that we explain in detail

a note on a nipotent lower bound of nipotent triangular norms abstract lower bounds of finite systems of nilpotent triangular norms are discussed by duality upper bounds of finite systems of nilpotent t conorms are found some applications are sketched

determination of the blow up rate for a critical semilinear wave equation in this paper we determine the blow up rate for the semilinear wave equation with critical power nonlinearity related to the conformal invariance

basic concepts for a theory of evaluation the aggregative operator abstract starting with an explication of the aggregative concept and deducing a general structure which satisfies a number of minimal requirements properties of clustering the main features of a new mathematical theory called theory of evaluation are developed the theory sheds new light on such well known concepts as membership conjunction and disjunction and seems to be a very promising tool to handle representation problems as they grow from the fields of theory of fuzzy set and its many applications of human decision making and of multicriteria analysis

triangular norm based iterative compensatory operators abstract aggregation operators based on a fixed t norm and on suitable transformations of processed data are introduced a special attention is paid to the class of iterative compensatory operators containing also the classical arithmetic geometric and harmonic means several properties of introduced operators are studied e g the symmetry the associativity the idempotency the anihilation etc several examples are given including continuous idempotent bisymmetric iterative compensatory operators with zero anihilator

the blow up rate for a non scaling invariant semilinear wave equations abstract we consider the semilinear wave equation 1 t 2 u u f u x t r n 0 t with f u u p 1 u log a 2 u 2 where p 1 and a r we show an upper bound for any blow up solution of 1 then in the one space dimensional case using this estimate and the logarithmic property we prove that the exact blow up rate of any singular solution of 1 is given by the ode solution associated with 1 namely u u p 1 u log a 2 u 2 unlike the pure power case g u u p 1 u the difficulties here are due to the fact that equation 1 is not scale invariant

existence and universality of the blow up profile for the semilinear wave equation in one space dimension in this paper we consider the semilinear wave equation with a power nonlinearity in one space dimension we exhibit a universal one parameter family of functions which stand for the blow up profile in self similar variables at a non characteristic point for general initial data the proof is done in self similar variables we first characterize all the solutions of the associated stationary problem as a one parameter family then we use energy arguments coupled with dispersive estimates to show that the solution approaches this family in the energy norm in the non characteristic case and to a finite decoupled sum of such a solution in the characteristic case finally in the case where this sum is reduced to one element which is the case for noncharacteristic points we use modulation theory coupled with a nonlinear argument to show the exponential convergence in the self similar time variable of the various parameters and conclude the proof this step provides us with a result of independent interest the trapping of the solution in self similar variables near the set of stationary solutions valid also for non characteristic points the proof of these results is based on a new analysis in the self similar variable 2007 elsevier inc all rights reserved

basic substructural core fuzzy logics and their extensions mianorm based logics abstract this paper addresses standard completeness for non associative non commutative substructural fuzzy logics and their axiomatic extensions first fuzzy systems which are based on mianorms binary monotonic identity aggregation operations on the real unit interval 0 1 their corresponding algebraic structures and algebraic completeness results are discussed next completeness with respect to algebras whose lattice reduct is 0 1 so called standard completeness is established for these systems using construction in the style of jenei montagna finally some axiomatic extensions of the non associative non commutative core fuzzy logics having axioms corresponding to the structural rule s of exchange and or associativity are considered

stable blowup for the cubic wave equation in higher dimensions abstract we consider the wave equation with a focusing cubic nonlinearity in higher odd space dimensions without symmetry restrictions on the data we prove that there exists an open set of initial data such that the corresponding solution exists in a backward light cone and approaches the ode blowup profile

incomplete blowup of solutions of quasilinear hyperbolic balance laws we study incomplete blowup of entropy solutions to first order quasilinear hyperbolic balance laws a general procedure to continue solutions beyond the blowup time which makes use of monotonicity methods is given the continuations thus obtained are possibly unbounded and satisfy suitable generalized entropy and rankine hugoniot conditions then the uniqueness of continuations satisfying such conditions is proved