... three ** mass ** ** functions ** corresponding to each modality, a confusion matrix ** of ** one versus ** the ** other can be formed ** The ** confusion-matrix ** of ** ** probability ** ** mass ** ** functions ** (PMFs), ** for ** this “N ” hypothesis problem ... formulation uses confusion matrices ** of ** ** probability ** ** mass ** ** functions ** Formulation ** of ** ** the ** two ** soft ** belief ** functions ** is discussed ﬁrst ** The ** ﬁrst belief function is suitable ** for ** binary hypothesis testing ... obtained ** for ** ** the ** audiovisual ** speech ** features combined is shown in Table 3.3 Formulating ** the ** ** Soft ** Belief Function Using ** the ** Confusion Matrix ** of ** ** Mass ** ** Functions ** ** The ** premise ** of ** coming up with such a confusion...

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... solving ** system ** ** of ** ** fractional-** order diﬀerential equations are based ** on ** two component procedure and polynomial initial condition The NHPM applied ** on ** fractionalorder Stiﬀ equation, ** fractional ** Genesio ... equations are found to follow as special cases ** of ** those ** of ** ** fractional-** order equations We consider the ** system ** ** of ** ** fractional-** order equations ** of ** the form Dαi yi t Fi t, y1 , y2 , y3 , , yn fi ... various kinds ** of ** nonlinear equations The new homotopy perturbation ** method ** NHPM was applied to linear and nonlinear ODEs 17 In this paper, we construct the solution ** of ** ** system ** ** of ** ** fractional-** order...

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... ** of ** higher-order ** generalized ** ** q-Genocchi ** ** numbers ** ** and ** ** polynomials ** attached to χ by using ** the ** generating function ** of ** those ** numbers ** ** and ** ** polynomials ** ** Generalized ** ** q-Genocchi ** ** Numbers ** ** and ** ** Polynomials ** For ... relation ** on ** ** the ** analogue ** of ** ** the ** Apostol-Bernoulli ** and ** ** the ** analogue ** of ** ** the ** Apostol-Genocchi ** polynomials,** ” Applied Mathematical Sciences, vol 3, no 53–56, pp 2757–2764, 2009 T Kim, **On ** ** the ** q-extension ... q-extension ** of ** Euler ** and ** Genocchi ** numbers,** ” Journal ** of ** Mathematical Analysis ** and ** Applications, vol 326, no 2, pp 1458–1465, 2007 L.-C Jang, “A study ** on ** ** the ** distribution ** of ** twisted ** q-Genocchi ** ** polynomials,** ”...

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... Inequalities and Applications Theorem 1.4 Under ** the ** conditions of Theorem 1.2, ** the ** assumptions EX ** for ** α / γ imply ** the ** following Marcinkiewicz-Zygmund ** strong ** law: −1 bn n ** for ** < α ≤ and 1.8 ani Xi ... and its application to probability theory,” Transactions of ** the ** American Mathematical Society, vol 82, pp 323–339, 1956 15 S H Sung, **On ** ** the ** ** strong ** convergence ** for ** ** weighted ** sumsof random variables,” ... we shall not only partially generalize Theorem D to ρ∗ -mixing case, but also extend Theorem B to ** the ** case αp ** The ** main purpose is to establish ** the ** MarcinkiewiczZygmund ** strong ** ** laws ** ** for ** linear statistics...

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... can be eliminated, ** and ** prove ** the ** superstability ** of ** ** quadratic ** ** double ** ** centralizers ** ** and ** ** quadratic ** multipliers ** on ** ** a ** Banach algebra by ** a ** method ** of ** ﬁxed ** point ** Journal ** of ** Inequalities ** and ** Applications ... is ** a ** ** quadratic ** homogeneous mapping ** and ** R ab ** a2** R b , for all ** a,** b ∈ ** A ** Also, ** a ** ** quadratic ** ** double ** centralizer ** of ** an algebra ** A ** is ** a ** pair L, R where L is ** a ** ** quadratic ** left centralizer, R is ** a ** ** quadratic ** ... L is ** a ** ** quadratic ** homogeneous mapping, that is L λ2 L ** a ** , for all ** a ** ∈ ** A ** ** and ** λ ∈ C, ** and ** L ab L ** a ** b2 , for all ** a,** b ∈ ** A ** is ** quadratic ** ** and ** L **a ** A mapping R : ** A ** → ** A ** is ** a ** ** quadratic ** right centralizer...

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... discussions were ** for ** ** boundary ** ** value ** ** problems ** ** of ** ordinary diﬀerential equation This paper studies ** the ** ** existence ** ** of ** ** solutions ** ** for ** ** the ** nonlinear two-point ** dynamic ** ** boundary ** ** value ** problem ** on ** time ... solution x t to ** the ** ** boundary ** ** value ** problem xΔΔ t λf t, xσ t , xΔ t , xΔ a 0, t ∈ a, ρ2 b Ì, x b Then ** the ** ** boundary ** ** value ** problem 1.2 has at least one solution in C2 a, b Proof ** The ** proof is ** the ** ... **On ** Green’s functions and positive ** solutions ** ** for ** ** boundary ** ** value ** ** problems ** ** on ** time scales,” Journal ** of ** Computational and Applied Mathematics, vol 141, no 1-2, pp 75–99, 2002, Special issue ** on ** “Dynamic...

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... involution ** on ** X We denote by ** C ** X, τ ** the ** set ** of ** all f ∈ ** C ** X for which f ◦ τ f Then ** C ** X, τ is a ** unital ** ** uniformly ** ** closed ** real subalgebra ** of ** ** C ** X which separates ** the ** points ** of ** X, does not contain ** the ** constant ... using ** the ** concept ** of ** τ-peak points for ** unital ** ** uniformly ** ** closed ** real ** subalgebras ** ** of ** ** C ** X, τ , we show that some ** of ** these algebras not have ** the ** ﬁxed-point ** property ** FPP ** of ** Complex ** Subalgebras ** ** of ** ** C ** X ... ﬁxed-point ** property ** Proof By part i ** of ** Proposition 3.4, CR X, τ is an inﬁnite dimensional real vector space ** On ** ** the ** other hand, CR X, τ is an inverse **-closed ** ** unital ** ** uniformly ** ** closed ** real ** subalgebras ** ** of ** CR...

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... xα ** and ** yα → y Main Results In this section, we apply Kakutani-Fan-Glicksberg ﬁxed-point theorem to prove an ** existence ** theorem ** of ** ** strong ** solutions ** for ** ** the ** ** system ** ** of ** ** generalized ** ** strong ** ** vector ** ** quasiequilibrium ** ... ** vector ** ** quasiequilibrium ** problem Many authors studied ** the ** ** existence ** ** of ** solutions ** for ** systems ** of ** ** vector ** ** quasiequilibrium ** ** problems,** see, ** for ** example, 19–23 ** and ** references therein ** On ** ** the ** other hand, ... solution see 13 Thus, it is important to study ** the ** ** existence ** ** of ** ** strong ** solution ** and ** properties ** of ** ** the ** ** strong ** solution set In general, ** the ** ideal solutions not exist Very recently, ** the ** ** generalized ** strong...

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... Journal of Inequalities and Applications Both of them are important ** in ** Mathematical Analysis and its applications It attracts some attention ** in ** recent years Actually, inequalities 1.1 and 1.2 have ... many generalizations and variations Equation 1.1 has been strengthened by Yang and others including double series inequalities 4–21 ** In ** 2008, Xie and Zeng gave ** a ** ** new ** ** Hilbert-type ** ** Inequality ** as ... integral ** inequality ** ** with ** ** a ** non-homogeneous form and ** a ** best constant factor,” Advances and Applications ** in ** Mathematical Science, vol 3, no 1, pp 61–71, 2010 Z Xie and Z Zeng, **The ** ** Hilbert-type ** integral...

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... weight function ** on ** a, b , and let g be ** an ** increasing function ** on ** a, b , α such that g is a continuous function ** on ** a, b and α > Ia ;g f denotes the left-sided fractional integral ** of ** a function f with ... let g be ** an ** increasing function ** on ** a, b and g a continuous function ** on ** a, b The leftand right-sided fractional integrals ** of ** a function f with respect to another function g in a, b are given by ... function ** on ** a, b , α such that g is a continuous function ** on ** a, b and α > Ib− ;g f denotes the right-sided fractional integral ** of ** a function f with respect to another function g in a, b Deﬁne v on...

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... purpose ** of ** this paper is to establish the general version ** of ** ** inequalities ** 1.7 and new ** Hadamard-type ** ** inequalities ** ** involving ** two log-convex functions, two m-convex functions, or two α, m -convex ... generalizations ** of ** the convexity,” in Proceedings ** of ** the Colloquium ** on ** Approximation and Optimization, pp 329–338, University ** of ** Cluj-Napoca, Cluj-Napoca, Romania V G Mihesan, “A generalization ** of ** the convexity,” ... m-concave if −f is m-convex Denote by Km b the class ** of ** all m-convex functions ** on ** 0, b such that f ≤ if m < Obviously, if we choose m 1, Deﬁnition 1.1 recaptures the concept ** of ** standard convex...

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... which concerns ** the ** ** exponent ** ** of ** ** convergence ** Theorem 2.1 Let B and C be entire functions ** of ** order less than with C ≡ and B being / transcendental Then every solution f / ** of ** ** the ** equation ≡ ** y ** ** Ay ** C z ... replaced ** by ** h A, arises if conclusion i ** of ** Lemma 4.4 holds, and ** the ** proof ** of ** ** the ** theorem is complete Acknowledgment ** The ** author thanks Professor J K Langley ** for ** ** the ** invaluable discussions ** on ** ** the ** results ... , A z ** By ** 0, α ∈ C \ {0}, 2.1 has ** zeros ** with inﬁnite ** exponent ** ** of ** ** convergence ** ** The ** hypothesis that B is transcendental is not redundant since Frei has shown that ** y ** e−z ** y ** Ky has ** solutions ** ** of ** ﬁnite...

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... ** Orlicz ** function ** and ** ¸ ideals ** in ** ** 2-normed ** ** spaces ** ** In ** this paper, we continue to study certain ** new ** ** sequence ** ** spaces ** by ** using ** ** Orlicz ** function ** and ** ideals ** in ** ** 2-normed ** ** spaces ** ** In ** this context it should ... Sahiner, M Gurdal, S Saltan, ** and ** H Gunawan, **Ideal ** ** convergence ** ** in ** ** 2-normed ** ** spaces,** ” Taiwanese ¸ ¨ Journal of Mathematics, vol 11, no 5, pp 1477–1484, 2007 M Gurdal ** and ** S Pehlivan, “Statistical ** convergence ** ... “Approximation theory ** in ** 2-Banach ** spaces,** ” Nonlinear Analysis: ¸ ¸ ¨ Theory, Methods & Applications, vol 71, no 5-6, pp 1654–1661, 2009 11 M A Krasnoselskii ** and ** Y B Rutisky, Convex Function ** and ** ** Orlicz ** ** Spaces,** ...

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... **On ** ** complete ** ** convergence ** ** for ** ** arrays ** ** of ** ** rowwise ** dependent ** random ** ** variables,** ” Statistics & Probability Letters, vol 77, no 11, pp 1050–1060, 2007 17 A Kuczmaszewska, **On ** ** complete ** ** convergence ** ** for ** ... ** arrays ** ** of ** negatively dependent ** random ** ** variables ** ** and ** ** its ** applications,” Journal ** of ** Theoretical Probability, vol 23, no 2, pp 362–377, 2010 19 S H Sung, **Complete ** ** convergence ** ** for ** weighted sums ** of ** ** random ** ... ** convergence ** ** for ** ** arrays ** ** of ** ** rowwise ** dependent ** random ** ** variables ** has been considered We refer to Kuczmaszewska 16 ** for ** ** ρ-mixing ** ** and ** ** ρ-mixing ** sequences, Kuczmaszewska 17 ** for ** negatively associated sequence, and...

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