... 1.6 hold ** for ** all a, b > with a / b Main Results Firstly, we present ** the ** ** optimal ** ** convex ** ** combination ** ** bounds ** of contraharmonic and geometric means ** for ** Seiﬀert’s mean as follows Theorem 2.1 ** The ** double ... implies that ** for ** any β1 < 1/π there exists X β1 C t2 , 2.22 β1 π < X β1 > such that − β1 G t2 , < P t2 , 2.23 ** for ** t ∈ X, ∞ Secondly, we present ** the ** ** optimal ** ** convex ** ** combination ** ** bounds ** of ** the ** contraharmonic ... M.-K Wang, and G.-D Wang, **The ** ** optimal ** ** convex ** ** combination ** ** bounds ** of arithmetic and harmonic means ** for ** ** the ** Seiﬀert’s mean,” Journal of Inequalities and Applications, ** Article ** ID 436457, pages, 2010...

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... Vasundhara Devi, Theory ** of ** ** Fractional ** Dynamic Systems, Cambridge Academic, Cambridge, UK, 2009 V Lakshmikantham and ** A ** S Vatsala, “Basic theory ** of ** ** fractional ** diﬀerential equations,” ** Nonlinear ** Analysis ... 2391–2396, 2009 17 H ** A ** H Salem, “On ** the ** ** nonlinear ** Hammerstein ** integral ** equations in Banach spaces and application ** to ** ** the ** ** boundary ** value problem ** of ** ** fractional ** order,” Mathematical and Computer Modelling, ... Zhang, **The ** ** existence ** ** of ** ** a ** ** positive ** ** solution ** for ** a ** ** nonlinear ** ** fractional ** diﬀerential ** equation,** ” Journal ** of ** Mathematical Analysis and Applications, vol 252, no 2, pp 804–812, 2000 22 S Zhang, “Existence...

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... e follows: sup|y|≤s u y Su u 1.2 M ** To ** obtain ** the ** supremum ** of ** S i.e., ** the ** ** best ** ** constant ** ** of ** ** Sobolev ** ** inequality ** , we consider ** the ** following ** clamped ** ** boundary ** ** value ** problem: −1 M u 2M f x −s < x ... −s, s Clearly, Theorem 1.2 i , ii is rewritten equivalently as follows Corollary 1.3 Let u ∈ H, then ** the ** ** best ** ** constant ** ** of ** ** Sobolev ** ** inequality ** **(corresponding ** ** to ** ** the ** embedding ** of ** H into L∞ −s, s ) ... 2 ** Boundary ** ** Value ** Problems ** The ** fact that ·, · M induces ** the ** equivalent norm ** to ** ** the ** standard norm ** of ** ** the ** ** Sobolev ** Hilbert space ** of ** Mth order follows from Poincar´ ** inequality ** Let us introduce the...

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... , ** and ** Kumam ** and ** Jaiboon 28 , we introduce a new ** shrinking ** ** projection ** ** method ** ** for ** ﬁnding a ** common ** element ** of ** ** the ** set ** of ** ﬁxed points ** of ** ** strictly ** ** pseudocontractive ** mappings, ** the ** set ** of ** ** common ** ** solutions ** ... approximation ** method ** ** for ** ﬁnding a ** common ** element ** of ** ** the ** set ** of ** ﬁxed ** point ** ** of ** ** strictly ** ** pseudocontractive ** mappings Journal ** of ** Inequalities ** and ** Applications ** and ** ** the ** set ** of ** ** solutions ** ** of ** variational ... In 2010, Kumam ** and ** Jaiboon 28 introduced a new ** method ** ** for ** ﬁnding a ** common ** element ** of ** ** the ** set ** of ** ﬁxed ** point ** ** of ** ** strictly ** ** pseudocontractive ** mappings, ** the ** set ** of ** ** common ** ** solutions ** ** of ** variational inequalities...

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... 3.6 ** For ** a suitable choice of ** the ** mappings A, η, F, M, Ik , and space X, then ** the ** ** Algorithm ** 3.5 can be degenerated to ** the ** hybrid proximal ** point ** ** algorithm ** 16, 17 and ** the ** ** over-relaxed ** ** A-proximal ** ** point ** ... generalized version of ** the ** ** over-relaxed ** proximal ** point ** ** algorithm ** and its applications to approximation solvability of ** the ** ** inclusion ** problem of ** the ** form 2.1 based on ** the ** A, η -accretive ** set-valued ** mapping ... denote ** the ** single-valued generalized duality mapping by Jq in real uniformly smooth Banach space X unless otherwise stated We consider ** the ** following ** general ** ** nonlinear ** ** mixed ** ** set-valued ** inclusion...

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... OPQ approach and ﬁnally concludes ** the ** paper ** Research ** Methods ** for ** ** Quality ** ** of ** ** Experience ** Evaluation 2.1 Psychoperceptual Evaluation Methods Psychoperceptual ** quality ** evaluation is ** a ** ** method ** ** for ** examining ... ** quality ** with ** the ** help ** of ** ** a ** set ** of ** ** quality ** attributes All methods assume that perceived ** quality ** is ** the ** result ** of ** ** a ** combination ** of ** several attributes and that these attributes can be rated by ** a ** ... Identiﬁcation ** of ** ** the ** Acceptance threshold Bars show means and standard deviation 12 5.1.2 Satisfaction with Overall ** Quality ** ** The ** test variables had signiﬁcant eﬀect on ** the ** overall ** quality ** when averaged...

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... generalize ** the ** concept ** of ** ** u0 ** ** **** -concave ** operators, give a concept ** of ** ** the ** ** generalized ** ** u0 ** ** **** -concave ** operators, and study ** the ** existence and uniqueness ** of ** ﬁxed points for this class ** of ** operators by ** the ** ** iterative ** ... doesn’t satisfy ** the ** deﬁnition ** of ** ** u0 ** ** **** -concave ** operators Therefore, we can’t obtain ** the ** ﬁxed point ** of ** A by ** the ** ﬁxed point theorem ** of ** ** u0 ** ** **** -concave ** operators ** The ** ** u0 ** ** **** -concave ** operators’ ﬁxed points ... | − **u0 ** ≤ x ≤ **u0 ** }, ** u0 ** 2.11 ∀x ∈ Eu0 It is easy to see that Eu0 becomes a normed linear space under ** the ** norm · ** the ** ** u0 ** - norm ** of ** ** the ** element x ∈ Eu0 see 3, ** u0 ** x ** u0 ** is called Theorem 2.4 Let...

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... this ** inequality ** is equivalent to ** Jensen’s ** ** inequality ** Qi − pi f xi Rk − pk f xk pk f pi pi xi pi pk xk pk 1.9 ≥ Qi Rk f Qi xi Qi Rk xk Rk Main Results Theorem 2.1 Let f be a convex function ** on ** ... numbers, and let f be a convex function ** on ** I If a, b, c, d ∈ I such that c, d ∈ a, b and pa qb pc qd, 2.4 then qf b ≥ pf c pf a qf d 2.5 Lemma 2.3 Let f be a convex function ** on ** I, and let x1 , x2 ... Applications Equality in 2.18 holds ** for ** a1 a2 · · · an If i √ ak , ak ak a1 a2 · · · , · · · ak−1 Remark 2.9 ** For ** p1 a1 a2 ··· p2 pn ** with ** equality if and only if a1 n 1, then equality holds again for...

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... with attack and release time constants τraise and τdecay ** The ** diﬀerences between ** the ** maxima and minima are calculated to obtain ** the ** current dynamic range ** of ** ** the ** signal (4) ** The ** decision for ** a ** ** speech ** ... vectors containing ** speech ** samples will be added to ** the ** noise data matrix in (5), which leads to cancellation ** of ** parts ** of ** ** the ** ** speech ** signal ** On ** ** the ** other hand, if too many actual noise samples are detected ... stationary directional noise and nonstationary diﬀuse noise ** The ** nonstationary noise is derived from recordings in ** a ** restaurant to approach ** a ** real world situation Section provides ** a ** discussion of...

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... virtual because it is mathematically motivated and based on ** the ** information in ** the ** state rather than an actual measurement ** The ** second factor of (6) can then be handled directly, using ** a ** ** particle ** ... for ** the ** ** particle ** ﬁlter, with ** the ** diﬀerence that when ** a ** ** particle ** is selected, so is ** the ** full state matching that ** particle,** as well as ** the ** covariance matrix describing ** the ** Kalman ﬁlter part of ** the ** ... associated covariance, and methods to update these (measurement and time update functions) In ** a ** similar manner, ** the ** PF object has particles and weights as internal data, and likelihood calculations,...

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... RDF using ** the ** JPEG coder on ** the ** Lena image ** under ** ** the ** MSE distortion measure For comparison we have also shown ** the ** ** high-resolution ** MSE-RDF (thin line) ** The ** horizontal axes on ** the ** top and ** the ** bottom ... that, ** under ** ** high-resolution ** assumptions, ** the ** RDF for a range of natural images ** under ** ** the ** commonly used SSIM index has a simple form In fact, ** the ** RDF only depends upon ** the ** diﬀerential entropy of ** the ** ... Matlab Then, we compare these operational results to ** the ** information theoretic estimated ** high-resolution ** SSIM RDF obtained as described in ** the ** previous section We are interested in ** the ** high-resolution...

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... Figure 4: ** The ** example ** of ** ** the ** position ** of ** ** the ** referent and assigned element ** of ** ** the ** nested HS function in ** the ** block-matrix in ** the ** space ** of ** ** the ** selected hyperspheric block-matrix According to ** the ** translator ... separately, and therefore we develop speciﬁc ** translators ** ** of ** ** the ** ϑ Δk, Δn, type On ** the ** basis ** of ** ** the ** established graph, all option relations are shaped There are in total thirty ** of ** them 10 × , and they are ... to ** the ** interpolating and other properties ** of ** ** the ** gamma function ** Functional ** operators deﬁned in ** the ** previously described way can be applied in deﬁning ** the ** total dimensional potential ** of ** ** the ** hyperspherical...

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... Diﬀerence ** Equations ** ** and ** uniqueness ** of ** ** the ** solutions to ** random ** ** impulsive ** diﬀerential ** equations,** ** and ** in 18 Zhao ** and ** Zhang discussed ** the ** ** exponential ** ** stability ** ** of ** ** random ** ** impulsive ** integro-diﬀerential ** equations ** ... equation ** of ** ** neutral ** type One ** of ** ** the ** main reason is that ** the ** methods to discuss ** the ** ** exponential ** ** stability ** ** of ** deterministic ** impulsive ** diﬀerential ** equations ** ** of ** ** neutral ** type ** and ** ** the ** ** exponential ** ** stability ** ... ** for ** ** random ** diﬀerential ** equations ** can not be directly adapted to ** the ** case ** of ** ** random ** ** impulsive ** diﬀerential ** equations ** ** of ** ** neutral ** type, especially, ** random ** ** impulsive ** integrodiﬀerential ** equations ** of...

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... functional response,” Journal ** of ** Mathematical Analysis ** and ** Applications, vol 281, no 1, pp 395–401, 2003 T K Kar ** and ** U K Pahari, “Modelling ** and ** analysis ** of ** ** a ** prey-predator ** system ** ** with ** stage-structure ... response,” Journal ** of ** Mathematical Analysis ** and ** Applications, vol 317, no 2, pp 464–474, 2006 D T Dimitrov ** and ** H V Kojouharov, “Complete mathematical analysis ** of ** ** predator-prey ** models ** with ** linear prey ... ** of ** Mathematical Analysis ** and ** Applications, vol 295, no 1, pp 15–39, 2004 10 X Yang, “Uniform persistence ** and ** periodic solutions for ** a ** ** discrete ** ** predator-prey ** ** system ** ** with ** delays,” Journal ** of ** Mathematical...

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... kind ** of ** ** boundary ** that is ** the ** Keldys-Fichera ** boundary ** ** value ** ** problem,** ** with ** that ** the ** associated ** problem ** is ** of ** well-posedness However, for higher-order ones, ** the ** discussion ** of ** well-posed ** boundary ** ** value ** ... is a generalization ** of ** 3, 8–10 |λ|≤m−1 |λ| 1.8 λ D gλ x, u , ** Boundary ** ** Value ** Problems Formulation ** of ** ** the ** ** Boundary ** ** Value ** ** Problem ** For second-order ** equations ** ** with ** ** nonnegative ** ** characteristic ** form, ... We need to check ** the ** reasonableness ** of ** ** the ** ** boundary ** ** value ** ** problem ** 2.10 – 2.13 under ** the ** deﬁnition ** of ** weak solutions, that is, ** the ** solution in ** the ** classical sense are necessarily ** the ** solutions in...

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