It is possible to compute j(tau) and its modular equations with no perception of its related classical group structure except at infinity. We start by taking, for p prime, an unknown ''p-Newtonian'' po...
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It is possible to compute j(tau) and its modular equations with no perception of its related classical group structure except at infinity. We start by taking, for p prime, an unknown ''p-Newtonian'' polynomial equation g(u, v) = 0 with arbitrary coefficients (based only on Newton's polygon requirements at infinity for u = j(tau) and v = j(pr)). We then ask which choice of coefficients of g(u, v) leads to some consistent Laurent series solution u = u(q) approximate to 1/q, v = u(q(p)) (where q = exp 2 pi i tau). It is conjectured that if the same Lament series u(q) works for p-Newtonian polynomials of two or more primes p, then there is only a bounded number of choices for the Laurent series (to within an additive constant). These choices are essentially from the set of ''replicable functions,'' which include more classical modular invariants, particularly u = j(tau). A demonstration for orders p = 2 and 3 is done by computation. More remarkably, if the same series u(q) works for the p-Newtonian polygons of 15 special ''Fricke-Monster'' values of p, then (u=)j(tau) is (essentially) determined uniquely. Computationally, this process stands alone, and, in a sense, modular invariants arise ''spontaneously.''
How protein structure encodes functionality is not fully understood For example, long-range intraprotein communication can occur without measurable conformational change and is often not captured by existing structura...
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How protein structure encodes functionality is not fully understood For example, long-range intraprotein communication can occur without measurable conformational change and is often not captured by existing structural correlation functions. It is shown here that important functional information is encoded in the timing of protein motions, rather than motion itself. I introduce the conditional activity function to quantify such tuning correlations among the degrees of freedom within proteins. For three proteins, the conditional activities between side-chain dihedral angles were computed using the output of microseconds-long atomistic simulations. The new approach demonstrates that a sparse fraction of side-chain pairs are dynamically correlated Over long distances (Tanning protein lengths up to 7 nm), in sharp contrast to structural Correlations, which are short-ranged (<1 nm). Regions of high self- and inter-side-chain dynamical correlations" are found, corresponding to experimentally determined functional modules and allosteric connections, respectively.
In this note, we present improved upper bounds on the circuit complexity of symmetric Boolean functions. In particular, we describe circuits of size 4.5n + o(n) for any symmetric function of n variables, as well as ci...
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In this note, we present improved upper bounds on the circuit complexity of symmetric Boolean functions. In particular, we describe circuits of size 4.5n + o(n) for any symmetric function of n variables, as well as circuits of size 3n for MOD3n function. (C) 2010 Elsevier B.V. All rights reserved.
We address the question to what extent polyhedral knowledge about individual knapsack constraints suffices or lacks to describe the convex hull of the binary solutions to their intersection. It turns out that the sign...
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We address the question to what extent polyhedral knowledge about individual knapsack constraints suffices or lacks to describe the convex hull of the binary solutions to their intersection. It turns out that the sign patterns of the weight vectors are responsible for the types of combinatorial valid inequalities appearing in the description of the convex hull of the intersection. In particular, we introduce the notion of an incomplete set inequality which is based on a combinatorial principle for the intersection of two knapsacks. We outline schemes to compute nontrivial bounds for the strength of such inequalities w.r.t. the intersection of the convex hulls of the initial knapsacks. An extension of the inequalities to the mixed case is also given. This opens up the possibility to use the inequalities in an arbitrary simplex tableau.
This paper proposes a gap-metric-based multiple model predictive control (MMPC) method for nonlinear systems with a wide operating range. The gap metric theory, integrated into a neighborhood estimation algorithm, is ...
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This paper proposes a gap-metric-based multiple model predictive control (MMPC) method for nonlinear systems with a wide operating range. The gap metric theory, integrated into a neighborhood estimation algorithm, is utilized to partition the whole operating range into subregions corresponding to operating points. A local controller is then designed in each subregion and is composed of a constant feedback control and a receding infinite-horizon control with an estimated polyhedral stable region. To guarantee the global stability of the whole system, we design a novel switching rule activating between local controllers. The simulation study on a continuous stirred-tank reactor (CSTR) is presented to validate the proposed methods.
The theory of modular spaces was initiated by H. Nakano in connection with the theory of order spaces and redefined and generalized by J. Musielak and W. Orlicz. Even though a metric is not defined, many problems in f...
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The theory of modular spaces was initiated by H. Nakano in connection with the theory of order spaces and redefined and generalized by J. Musielak and W. Orlicz. Even though a metric is not defined, many problems in fixed point theory for nonexpansive mappings can be reformulated in modular spaces. The existence of fixed points for a more general class of mappings namely uniformly Lipschitzian mappings is studied.
Five-axis machining of free-form surfaces has one major advantage over three-axis machining, i.e. a greater degree of flexibility in positioning the cutting tool relative to the surface. In five-axis machining of free...
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Five-axis machining of free-form surfaces has one major advantage over three-axis machining, i.e. a greater degree of flexibility in positioning the cutting tool relative to the surface. In five-axis machining of free-form surfaces there are three major phases in creating the tool path: (i) generation of the cutter contact (CC) points;(ii) formation of the cutter location (CL) points that define the path followed by the cutting tool reference point;and (iii) the creation of the specific machine tool part program (G-code file). In this paper, the free-form surface is defined as a triangular polyhedral mesh. The CC-points are created from the surface mesh definition employing a cutting plane technique. Additionally, the CC points are positioned based on an examination of several important factors: geometric constraints derived from the machine tool axis limits, gouging (undercutting) of the free-form surface by the cutting tool and collision of the tool with either the machining stock or machine. The CL points can then be generated along the resulting CC points by consideration of specific machining strategies, such as cusp height and a smooth change in tool posture. The critical issues addressed in this work concern the avoidance of machining problems (machine limit, collision, and gouging) in the tool-path generation phase. Therefore, this technique avoids inefficient five-axis machining practices by automatically creating and verifying a feasible tool-path prior to the actual metal cutting.
The values taken by Gamma(0)(n)-modular functions at elliptic points of order 2 for the Fricke group Gamma(0)(n)(+) that lie outside Gamma(0)(n) are studied. In the case of a principal modulus ('Hauptmodul') f...
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The values taken by Gamma(0)(n)-modular functions at elliptic points of order 2 for the Fricke group Gamma(0)(n)(+) that lie outside Gamma(0)(n) are studied. In the case of a principal modulus ('Hauptmodul') for Gamma(0)(n) or Gamma(0)(n)(+), the class fields generated by these values are determined.
In 2015 Choi, Kim, and Lovejoy studied a weighted partition function, A(1) (m), which counted subpartitions with a structure related to the Rogers-Ramanujan identities. They conjectured the existence of an infinite cl...
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In 2015 Choi, Kim, and Lovejoy studied a weighted partition function, A(1) (m), which counted subpartitions with a structure related to the Rogers-Ramanujan identities. They conjectured the existence of an infinite class of congruences for A(1) (m), modulo powers of 5. We give an explicit form of this conjecture, and prove it for all powers of 5. (C) 2018 Elsevier Inc. All rights reserved.
Given an ordinary elliptic curve E/ k : y 0 2 = x & oacute;+ a 0 x 0 + b 0 over a field k of characteristic p >= 5 with j -invariant j 0 , the j -invariant of its canonical lifting E / W ( k) : y 2 = x 3 + ax +...
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Given an ordinary elliptic curve E/ k : y 0 2 = x & oacute;+ a 0 x 0 + b 0 over a field k of characteristic p >= 5 with j -invariant j 0 , the j -invariant of its canonical lifting E / W ( k) : y 2 = x 3 + ax + b is j = ( j 0 , J 1 ( j 0 ) , J 2 ( j 0 ) , . . . ), for some J i is an element of F p ( X ). Thus the Weierstrass coefficients of E can be given by a = lambda 4 27 j / (6912 - 4 j ), b = lambda 6 27 j / (6912 - 4 j ), where lambda = (( b 0 /a 0 ) 1/ 2 , 0 , 0 , ... ), and therefore can be seen as functions on ( a 0 , b 0 ). Here we study the denominators of the coordinates of these a and b . We show that the only possible factors for these denominators are powers of a 0 , b 0 , and the Hasse invariant h . Upper bounds for these powers are given for each one of them. (c) 2024 Elsevier Masson SAS.
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