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    Operator Relations for SU(3) Breaking Contributions to K and K* Distribution Amplitudes

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    We derive constraints on the asymmetry a1 of the momentum fractions carried by quark and antiquark in K and K* mesons in leading twist. These constraints follow from exact operator identities and relate a1 to SU(3) breaking quark-antiquark-gluon matrix elements which we determine from QCD sum rules. Comparing our results to determinations of a1 from QCD sum rules based on correlation functions of quark currents, we find that, for a1^\parallel(K*) the central values agree well and come with moderate errors, whereas for a1(K) and a1^\perp(K*) the results from operator relations are consistent with those from quark current sum rules, but come with larger uncertainties. The consistency of results confirms that the QCD sum rule method is indeed suitable for the calculation of a1. We conclude that the presently most accurate predictions for a1 come from the direct determination from QCD sum rules based on correlation functions of quark currents and are given by: a1(K) = 0.06\pm 0.03, a1^\parallel(K*) = 0.03\pm 0.02, a1^\perp(K*) = 0.04\pm 0.03.Comment: 21 page

    Gas Phase Train in Upstream Oil and Gas Fields: PART-III Control Systems Design

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    This paper presents and implements a control structure solution based on MPC for two control problems affecting gas phase train in the existing oil and gas production plants:The disturbance growth in the series connected process and the control system dependency onoperators. This work examines the integration of small size MPC’s with the classical PID control system to handle interactive control loops in three series gas treatment processes

    Tumor-targeting Salmonella typhimurium A1-R inhibits human prostate cancer experimental bone metastasis in mouse models.

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    Bone metastasis is a frequent occurrence in prostate cancer patients and often is lethal. Zoledronic acid (ZOL) is often used for bone metastasis with limited efficacy. More effective models and treatment methods are required to improve the outcome of prostate cancer patients. In the present study, the effects of tumor-targeting Salmonella typhimurium A1-R were analyzed in vitro and in vivo on prostate cancer cells and experimental bone metastasis. Both ZOL and S. typhimurium A1-R inhibited the growth of PC-3 cells expressing red fluorescent protien in vitro. To investigate the efficacy of S. typhimurium A1-R on prostate cancer experimental bone metastasis, we established models of both early and advanced stage bone metastasis. The mice were treated with ZOL, S. typhimurium A1-R, and combination therapy of both ZOL and S. typhimurium A1-R. ZOL and S. typhimurium A1-R inhibited the growth of solitary bone metastases. S. typhimurium A1-R treatment significantly decreased bone metastasis and delayed the appearance of PC-3 bone metastases of multiple mouse models. Additionally, S. typhimurium A1-R treatment significantly improved the overall survival of the mice with multiple bone metastases. The results of the present study indicate that S. typhimurium A1-R is useful to prevent and inhibit prostate cancer bone metastasis and has potential for future clinical use in the adjuvant setting

    Linear equations with unknowns from a multiplicative group whose solutions lie in a small number of subspaces

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    Let K be a field of characteristic 0. We consider linear equations a1*x1+...+an*xn=1 in unknowns x1,...,xn from G, where a1,...,an are non-zero elements of K, and where G is a subgroup of the multiplicative group of non-zero elements of K. Two tuples (a1,...,an) and (b1,...,bn) of non-zero elements of K are called G-equivalent if there are u1,...,un in G such that b1=a1*u1,..., bn=an*un. Denote by m(a1,...,an,G) the smallest number m such that the set of solutions of a1*x1+...+an*xn=1 in x1,...,xn from G is contained in the union of m proper linear subspaces of K^n. It is known that m(a1,...,an,G) is finite; clearly, this quantity does not change if (a1,...,an) is replaced by a G-equivalent tuple. Gyory and the author proved in 1988 that there is a constant c(n) depending only on the number of variables n, such that for all but finitely many G-equivalence classes (a1,...,an), one has m(a1,...,an,G)< c(n). It is as yet not clear what is the best possible value of c(n). Gyory and the author showed that c(n)=2^{(n+1)!} can be taken. This was improved by the author in 1993 to c(n)=(n!)^{2n+2}. In the present paper we improve this further to c(n)=2^{n+1}, and give an example showing that c(n) can not be smaller than n.Comment: 12 pages, latex fil

    Strongly intersecting integer partitions

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    We call a sum a1+a2+• • •+ak a partition of n of length k if a1, a2, . . . , ak and n are positive integers such that a1 ≤ a2 ≤ • • • ≤ ak and n = a1 + a2 + • • • + ak. For i = 1, 2, . . . , k, we call ai the ith part of the sum a1 + a2 + • • • + ak. Let Pn,k be the set of all partitions of n of length k. We say that two partitions a1+a2+• • •+ak and b1+b2+• • •+bk strongly intersect if ai = bi for some i. We call a subset A of Pn,k strongly intersecting if every two partitions in A strongly intersect. Let Pn,k(1) be the set of all partitions in Pn,k whose first part is 1. We prove that if 2 ≤ k ≤ n, then Pn,k(1) is a largest strongly intersecting subset of Pn,k, and uniquely so if and only if k ≥ 4 or k = 3 ≤ n ̸∈ {6, 7, 8} or k = 2 ≤ n ≤ 3.peer-reviewe

    Sum of squared logarithms - An inequality relating positive definite matrices and their matrix logarithm

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    Let y1, y2, y3, a1, a2, a3 > 0 be such that y1 y2 y3 = a1 a2 a3 and y1 + y2 + y3 >= a1 + a2 + a3, y1 y2 + y2 y3 + y1 y3 >= a1 a2 + a2 a3 + a1 a3. Then the following inequality holds (log y1)^2 + (log y2)^2 + (log y3)^2 >= (log a1)^2 + (log a2)^2 + (log a3)^2. This can also be stated in terms of real positive definite 3x3-matrices P1, P2: If their determinants are equal det P1 = det P2, then tr P1 >= tr P2 and tr Cof P1 >= tr Cof P2 implies norm(log P1) >= norm(log P2), where log is the principal matrix logarithm and norm(P) denotes the Frobenius matrix norm. Applications in matrix analysis and nonlinear elasticity are indicated
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