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Device independent playground investigating and opening up a quantum black box
... states, measurements, or even the dimension of the physical system However, we assume that the physical system obeys the law of quantum physics The reason we still assume quantum physics is simply ... allows us to focus on deterministic strategies for all contents and purposes Let us then derive a necessary condition for all LHV models to satisfy Consider the simplest scenario, a (2222) or CHSH ... assessment of quantum resources In particular, this work focuses on ”self testing”, that is the certification of the states and measurement operators inside a black box, solely based on the observable...
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Jensen’s Inequality
... and this last expression is the value of the European derivative security Of course, the LHS cannot be strictly less than the RHS above, since stopping at time n is always allowed, and we conclude ... g S = IE 1 + r ,n g Sn : 94 S2 (HH) = 16 S (H) = S2 (HT) = S =4 S2 (TH) = S1 (T) = S2 (TT) = Figure 7.3: A three period binomial model 7.3 Stopped Martingales Let fYk gn=0 be a stochastic ... American call Assume that r Consider the American derivative security with payoff g Sk in period k The value of this security is the same as the value of the simple European derivative security...
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Báo cáo hóa học: " On Minkowski’s inequality and its application" doc
... exponents are equal, i.e., 1/p = (1 /s + 1/t)/2 On the other hand, by using Minkowski s inequality for s >1 and t >1, respectively, we obtain 1 /s 1 /s ≤ (f (x) + g(x) )s dx f s (x)dx 1 /s + gs (x)dx ... (p−t)/ (s t) [(f (x) + g(x) )s ] (f (x) + g(x))p dx = · [(f (x) + g(x))t ] (s p)/ (s t) dx By using Hölder s inequality (see [1] or [2]) with indices (s - t)/(p - t) and (s - t)/ (s p), we have (p−t)/ (s t) ... reversed form of inequality (2.6) Acknowledgements The authors wish to thank the referee for his many excellent suggestions for improving the original manuscript This Research is supported by National...
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Báo cáo hóa học: " Extension of Hu Ke’s inequality and its applications Jing-Feng Tian" pptx
... Beckenbach-type inequality that is due to Wang [32] The rest of this paper is organized as follows In Section 2, we present extensions of (3) and (4) and establish their corresponding reversed versions In Section ... (27) The classical arithmetic-geometric mean inequality is one of the most important inequalities in analysis This classical inequality has been widely studied by many authors, and it has motivated ... purpose of this work is to give extensions of inequalities (3) and (4) and establish their corresponding reversed versions Moreover, the obtained results will be applied to improve Hao Z-C inequality...
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Báo cáo hóa học: " A new interpretation of Jensen’s inequality and geometric properties of -means" pptx
... − s2 = s1 λc,ϕ,ψ (x) + − s1 λc, s1 , s2 (x) = for each x Î I\{c} Therefore, we have λc, s1 , s2 (x) = s2 λc,ϕ,ψ (x) + − s2 (s1 = 0) (3) and λc, s1 , s2 (x) = s2 s − s1 − s1 s1 λc,ϕ,ψ (x) − s1 ... result asserts that a -mean function: ∇ ® M (f) is well defined and order preserving, and this assertion simultaneously gives a new interpretation of Jensen s inequality However, this assertion ... by Jensen s inequality This also means M (f) ≤ M ψ (f) because ψ is monotone decreasing on I For the strict case, since g is a non-constant function on Ω, we obtain the desired results from...
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Báo cáo hóa học: " On improvements of the Rozanova’s inequality" potx
... (1:5) The inequality (1.5) will be called as Rozanova s inequality in the paper Opial s inequality and its generalizations, extensions and discretizations play a fundamental role in establishing ... following inequality holds a b α β |D1 D2 x (s, t)| D1 D2 p (s, t) ∂ |x (s, t)| f p (s, t) · g ∂t p (s, t) |D1 D2 x (s, t)| b dsdt β D1 D2 p (s, t) · g D1 D2 p (s, t) D1 D2 p (s, t) · g a α ≤f s Proof Let y (s, ... D1 D2 x (s, t) )dsdt ≤ w b D1 D2 x (s, t) dsdt 0 Acknowledgements The authors express their deep gratitude to the referees for their many very valuable suggestions and comments The research of...
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Báo cáo hóa học: " Research Article The Best Lower Bound Depended on Two Fixed Variables for Jensen’s Inequality with Ordered Variables" pot
... Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993 S S Dragomir, J Peˇ ari´ , and L E Persson, “Properties of some functionals related to Jensen s c c inequality, ” ... Rk xk Since Qi pi ··· pk−1 Rk 1, this inequality is a consequence of Jensen s inequality Thus, the proof is completed 4.3 10 Journal of Inequalities and Applications Proof of Propositions Proof ... Inequalities and Applications 11 Since this inequality is homogeneous in and ak , and also in Qi and Rk , we may set and Qi Using the notations ak x and Rk p, where x ≥ and p > 0, the inequality is equivalent...
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Báo cáo sinh học: " Research Article Improvement and Reversion of Slater’s Inequality and Related Results" pdf
... special case of s1 s2 /2 if s1 < s2 and for t s1 , r s2 , and s s1 s2 /2 if 3.39 for t s1 , s s2 , r s2 < s1 Similarly by setting m in 3.44 , we have special case of 3.40 for r s1 , s s2 , s1 s2 /2 ... special case of s1 s2 /2 if s1 < s2 and for t s1 , r s2 , and s s1 s2 /2 3.28 for t s1 , s s2 , and r if s2 < s1 Similarly by setting m in 3.36 , we have special case of 3.29 for r s1 , s s1 s2 /2 ... every sk ∈ R, k ∈ {1, 2, 3, , m}, the matrices K sk sl /2, s1 m , K sk sl /2, s1 s2 /2 m are positive semi-definite matrices Particularly k,l k,l det K det K sl sk sk m , s1 sl s1 , k,l s2 ≥...
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Báo cáo hóa học: " Research Article On the Strengthened Jordan’s Inequality" pot
... previous research on Jordan s inequality, in this paper, we present two methods of sharpening Jordan s inequality The first method shows that one can obtain new strengthened Jordan s inequalities from ... the first author established an identity which states that the function sin x/x is a power series of (π − 4x2 ) with positive coefficients for all x = This enables us to obtain a much better inequality ... is also strict By choosing proper functions in Lemma 3.1, we sharpen Jordan s inequality as follows First, define the functions f1 (x) and f3 (x) by f1 (x) = sin x f1 (0) = , x f3 (x) = sin x...
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Báo cáo hóa học: " Research Article A Generalized Wirtinger’s Inequality with Applications to a Class of Ordinary Differential Equations" docx
... Inequalities and Applications For the special case that n and p 1, various problems on the solutions of 1.1 , such as the existence of periodic solutions, bifurcations of periodic solutions, and stability ... p is also considered by a lot of researchers see 7–13 Most of the work contained in literature on 1.1 is the existence and multiplicity of periodic solutions However, except the questions of ... differential equation 1.2 has been done to the best of the author knowledge Motivated by these cases, as a part of this paper, we study the estimates of periods of periodic solutions for the differential...
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Báo cáo hóa học: " Research Article A Hilbert’s Inequality with a Best Constant Factor" doc
... constant factors, K and K p of 3.1 and 3.2 , are the best possible Proof We only prove that K is the best possible If the constant factor K in 3.1 is not the best possible, then there exists a ... this paper is to build a new Hilbert s inequality with a best constant factor and some parameters In the following, we always suppose that 1/p 1/q 1, p > 1, a ≥ 0, −1 < α < 1, both functions u ... of Inequalities and Applications In 2006, Yang gave an extension of as follows If p > 1, 1/p 1/q 1, r > 1, 1/r 1 /s 1, t ∈ 0, , − min{r, s} t min{r, s} ≥ λ > p q − min{r, s} t, such that ∞ > ∞...
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Báo cáo hóa học: " Research Article Jensen’s Inequality for Convex-Concave Antisymmetric Functions and Applications" pptx
... Inequalities and Applications holds for every x, y ∈ I It is clear that every convex function is Jensen-convex To see that the class of convex functions is a proper subclass of Jensen-convex functions, ... proof, see 2, page 71 or 1, page 53 A class of functions which is between the class of convex functions and the class of Jensen-convex functions is the class of Wright-convex functions A function ... and J Peˇ ari´ , “Generalizations of the Jensen inequality, ” Osterreichische Akademie der c c c Wissenschaften Mathematisch-Naturwissenschaftliche Klasse Sitzungsberichte, vol 196, no 1–3, pp...
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Báo cáo hóa học: " Research Article Diamond-α Jensen’s Inequality on Time Scales" pdf
... ♦α s − a h s g s ♦α s b a h s ♦α s h s ♦α s f t a b hs f g s − f t ♦α s a ≥ at 3.8 b hs g s −t ♦α s a b at a b at b h s g s ♦α s − t h s ♦α s a h s g s ♦α s − a This leads to the desired inequality ... f t h s g β s ♦α s b a h s ♦α s h s ♦α s , if β < or β > 1; 3.11 , if β ∈ 0, ln t on 0, ∞ One can also see that f is concave h s |g s ♦α s b a h s ♦α s ≥ b a h s ln g s ♦α s b a h s ♦α s 3.12 ... thesis see also 8, In Section 3, we present our main results which are generalizations of Jensen s inequality on time scales Some examples and applications are given in Section Preliminaries...
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Báo cáo hóa học: " Research Article A Refinement of Jensen’s Inequality for a Class of Increasing and Concave Functions" pptx
... for various unknown weight vectors p This is why the statement of Theorem 1.2 makes the assumption that this is true for all possible weight vectors The following lemma gives a simple sufficient ... 1.14 k Define the set S by S p1 , , pn | pk ≥ 0, ∀k 1.15 We wish to show h p ≥ on the set S subject to the constraint p1 · · · pn Suppose the minimum of h p is in the interior of S By the Lagrange ... decreasing linear function of y Under the assumption that f y is strictly convex, there can be at most two solutions to the equation We will show that, under suitable conditions, there is at most...
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Báo cáo hóa học: " Research Article Some New Results Related to Favard’s Inequality" pot
... function see 4, page Lemma 1.9 If φ is convex on an interval I ⊆ R, then φ s1 s3 − s2 φ s2 holds for every s1 < s2 < s3 , s1 , s2 , s3 ∈ I Now, we will give our main results s1 − s3 φ s3 s2 − s1 ≥ ... Jensen sense for s ≥ Note that s f is continuous for s ≥ since lim s f s 0 Δ0 f and lim s f s 1 Δ1 f 2.10 This implies s f is continuous; therefore, it is log-convex Since s f is log-convex, ... Functions, Partial Orderings, and Statistical Applications, c c vol 187 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1992 S Karlin and W J Studden, Tchebycheff Systems:...
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Báo cáo hóa học: " Research Article Hilbert’s Type Linear Operator and Some Extensions of Hilbert’s Inequality" docx
... when ε is sufficiently small, which contradicts the hypothesis Hence the constant factor D(A,B) in (2.6) is the best possible and T = D(A,B) This completes the proof ∞ Theorem 2.3 Suppose that ... max {x, y } and give some new generalizations of Hilbert s inequality As applications, we also consider some particular results Yongjin Li et al Main results and applications Lemma 2.1 Define the ... Assume that the constant factor D(A,B) in (2.6) is not the best possible, then there exist a positive real number K Journal of Inequalities and Applications with K < D(A,B), such that (2.6) is...
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Báo cáo hóa học: " Research Article Hilbert’s Type Linear Operator and Some Extensions of Hilbert’s Inequality" doc
... when ε is sufficiently small, which contradicts the hypothesis Hence the constant factor D(A,B) in (2.6) is the best possible and T = D(A,B) This completes the proof ∞ Theorem 2.3 Suppose that ... max {x, y } and give some new generalizations of Hilbert s inequality As applications, we also consider some particular results Yongjin Li et al Main results and applications Lemma 2.1 Define the ... Assume that the constant factor D(A,B) in (2.6) is not the best possible, then there exist a positive real number K Journal of Inequalities and Applications with K < D(A,B), such that (2.6) is...
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Báo cáo hóa học: " Research Article New Strengthened Carleman’s Inequality and Hardy’s Inequality" ppt
... + 1/2 c (2.2) holds Furthermore, 4c/3 − 1/2 is the best constant in inequality (2.1) or 4c/3 + 1/2 is the best constant in inequality (2.2) Proof (i) We construct a function as f (x) = x ln + ... [11] S Kaijser, L.-E Persson, and A Oberg, “On Carleman and Knopp s inequalities,” Journal of Approximation Theory, vol 117, no 1, pp 140–151, 2002 [12] M Johansson, L.-E Persson, and A Wedestig, ... Mathematical Analysis and Applications, vol 253, no 2, pp 691–694, 2001 [8] X.-J Yang, “Approximations for constant e and their applications,” Journal of Mathematical Analysis and Applications, vol 262,...
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Báo cáo hóa học: " Research Article New Strengthened Carleman’s Inequality and Hardy’s Inequality" docx
... + 1/2 c (2.2) holds Furthermore, 4c/3 − 1/2 is the best constant in inequality (2.1) or 4c/3 + 1/2 is the best constant in inequality (2.2) Proof (i) We construct a function as f (x) = x ln + ... [11] S Kaijser, L.-E Persson, and A Oberg, “On Carleman and Knopp s inequalities,” Journal of Approximation Theory, vol 117, no 1, pp 140–151, 2002 [12] M Johansson, L.-E Persson, and A Wedestig, ... Mathematical Analysis and Applications, vol 253, no 2, pp 691–694, 2001 [8] X.-J Yang, “Approximations for constant e and their applications,” Journal of Mathematical Analysis and Applications, vol 262,...
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Báo cáo hóa học: "Research Article On the Precise Asymptotics of the Constant in Friedrich’s Inequality for Functions " potx
... fact this was our original interest in the subject The paper is organized as follows In Section 2, we present and discuss our main results In Section 3, these results are proved via some auxiliary ... will be established Hence, it is possible to construct the lower and the upper bounds for Kε Proofs of the main results and some auxiliary results In Sections 3.1 and 3.2 we discuss, present, and ... a set diameter εδ(ε) contained in a ball of radius δ(ε) Here we assume that δ(ε) = o(εn−2 ) as ε→0 Also we suppose that Γε = Γε ∪ S In this case our main result reads as follows Theorem 2.3 Suppose...
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