scholarly journals Reducing the 0-1 Knapsack Problem with a Single Continuous Variable to the Standard 0-1 Knapsack Problem

2012 ◽  
Vol 3 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Marcel Büther ◽  
Dirk Briskorn
Keyword(s):  
Knapsack Problem ◽  
Upper Bound ◽  
Original Problem ◽  
Natural Extension ◽  
Continuous Variable ◽  
Computational Effort ◽  
Objective Value ◽  
The One

The 0-1 knapsack problem with a single continuous variable (KPC) is a natural extension of the binary knapsack problem (KP), where the capacity is not any longer fixed but can be extended which is expressed by a continuous variable. This variable might be unbounded or restricted by a lower or upper bound, respectively. This paper concerns techniques in order to reduce several variants of KPC to KP which enables the authors to employ approaches for KP. The authors propose both, an equivalent reformulation and a heuristic one bringing along less computational effort. The authors show that the heuristic reformulation can be customized in order to provide solutions having an objective value arbitrarily close to the one of the original problem.

Structure Information From Electron Diffraction Intensities

1990 ◽  
Vol 48 (2) ◽  
pp. 516-517
Author(s):  
J. Gjønnes ◽  
N. Bøe ◽  
K. Gjønnes
Keyword(s):  
Computational Effort ◽  
Unit Cell ◽  
Small Unit ◽  
Structure Information ◽  
Dispersion Surface ◽  
Integrated Intensity ◽  
The One ◽  
Image Position ◽  
Convergent Beam ◽  
Beam Patterns

Structure information of high precision can be extracted from intentsity details in convergent beam patterns like the one reproduced in Fig 1. From low order reflections for small unit cell crystals,bonding charges, ionicities and atomic parameters can be derived, (Zuo, Spence and O’Keefe, 1988; Zuo, Spence and Høier 1989; Gjønnes, Matsuhata and Taftø, 1989) , but extension to larger unit cell ma seem difficult. The disks must then be reduced in order to avoid overlap calculations will become more complex and intensity features often less distinct Several avenues may be then explored: increased computational effort in order to handle the necessary many-parameter dynamical calculations; use of zone axis intensities at symmetry positions within the CBED disks, as in Figure 2 measurement of integrated intensity across K-line segments. In the last case measurable quantities which are well defined also from a theoretical viewpoint can be related to a two-beam like expression for the intensity profile:With as an effective Fourier potential equated to a gap at the dispersion surface, this intensity can be integrated across the line, with kinematical and dynamical limits proportional to and at low and high thickness respctively (Blackman, 1939).

scholarly journals A BOUND FOR THE INDEX OF A QUADRATIC FORM AFTER SCALAR EXTENSION TO THE FUNCTION FIELD OF A QUADRIC

2018 ◽  
Vol 19 (2) ◽  
pp. 421-450 ◽  
Author(s):  
Stephen Scully
Keyword(s):  
Quadratic Form ◽  
Upper Bound ◽  
Function Field ◽  
The Other ◽  
Direct Generalization ◽  
Other Hand ◽  
General Field ◽  
The One ◽  
Anisotropic Quadratic Form

Let $q$ be an anisotropic quadratic form defined over a general field $F$. In this article, we formulate a new upper bound for the isotropy index of $q$ after scalar extension to the function field of an arbitrary quadric. On the one hand, this bound offers a refinement of an important bound established in earlier work of Karpenko–Merkurjev and Totaro; on the other hand, it is a direct generalization of Karpenko’s theorem on the possible values of the first higher isotropy index. We prove its validity in two key cases: (i) the case where $\text{char}(F)\neq 2$, and (ii) the case where $\text{char}(F)=2$ and $q$ is quasilinear (i.e., diagonalizable). The two cases are treated separately using completely different approaches, the first being algebraic–geometric, and the second being purely algebraic.

Planar generalized electrodynamics for one-loop amplitude in the Heisenberg picture

2021 ◽  
pp. 2150142
Author(s):  
David Montenegro ◽  
B. M. Pimentel
Keyword(s):  
Gauge Invariance ◽  
Quantum Electrodynamics ◽  
Mass Shell ◽  
Natural Extension ◽  
Quantum Model ◽  
Covariant Quantization ◽  
Heisenberg Picture ◽  
Maxwell Electrodynamics ◽  
Loop Amplitude ◽  
The One

We examine the generalized quantum electrodynamics as a natural extension of the Maxwell electrodynamics to cure the one-loop divergence. We establish a precise scenario to discuss the underlying features between photon and fermion where the perturbative Maxwell electrodynamics fails. Our quantum model combines stability, unitarity, and gauge invariance as the central properties. To interpret the quantum fluctuations without suffering from the physical conflicts proved by Haag’s theorem, we construct the covariant quantization in the Heisenberg picture instead of the Interaction one. Furthermore, we discuss the absence of anomalous magnetic moment and mass-shell singularity.

Indentation of a Transversely Isotropic Thermoporoelastic Half-Space by a Rigid Circular Cylindrical Punch

2017 ◽  
Vol 84 (11) ◽  
Author(s):  
Yilan Huang ◽  
Guozhan Xia ◽  
Weiqiu Chen ◽  
Xiangyu Li
Keyword(s):  
Half Space ◽  
Original Problem ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
The Finite Element Method ◽  
Thermal Fields ◽  
Cylindrical Punch ◽  
The One ◽  
Physical Quantities ◽  
Potential Theory Method

Exact solutions to the three-dimensional (3D) contact problem of a rigid flat-ended circular cylindrical indenter punching onto a transversely isotropic thermoporoelastic half-space are presented. The couplings among the elastic, hydrostatic, and thermal fields are considered, and two different sets of boundary conditions are formulated for two different cases. We use a concise general solution to represent all the field variables in terms of potential functions and transform the original problem to the one that is mathematically expressed by integral (or integro-differential) equations. The potential theory method is extended and applied to exactly solve these integral equations. As a consequence, all the physical quantities of the coupling fields are derived analytically. To validate the analytical solutions, we also simulate the contact behavior by using the finite element method (FEM). An excellent agreement between the analytical predictions and the numerical simulations is obtained. Further attention is also paid to the discussion on the obtained results. The present solutions can be used as a theoretical reference when practically applying microscale image formation techniques such as thermal scanning probe microscopy (SPM) and electrochemical strain microscopy (ESM).

ON CONDENSATION IN NON-IDEAL BOSE GAS

1989 ◽  
Vol 03 (06) ◽  
pp. 471-478
Author(s):  
D.P. SANKOVICH
Keyword(s):  
Critical Temperature ◽  
Low Temperature ◽  
Upper Bound ◽  
Bose Gas ◽  
The One ◽  
Ideal Bose Gas

A model of the non-ideal Bose gas is considered. We prove the existence of condensate in the model at sufficiently low temperature. The method of majorizing estimates for the Duhamel Two Point Functions is used. The equation for the critical temperature and the upper bound for the one-particle excitations energy are obtained.

scholarly journals The Stranger as Friend: The Poetics of Friendship in Homer, Dante, and Boccaccio

2013 ◽  
Author(s):  
Franco Masciandaro
Keyword(s):  
Jacques Derrida ◽  
Emmanuel Levinas ◽  
Natural Extension ◽  
Divine Comedy ◽  
The Other ◽  
Maurice Blanchot ◽  
Philosophical Method ◽  
The Divine Comedy ◽  
The One ◽  
The Stranger

The principal aim of this study is to participate in the current renewed discourse on the meaning of friendship, initiated in 1994 by the French philosopher Jacques Derrida with his Politics of Friendship, by combining the philosophical method of inquiry with the hermeneutical approach to poetic representations of friendship in the Iliad, the Divine Comedy, and the Decameron. It examines friendship not only as the unique love between two persons based on familiarity and proximity, but as the love for the one who is far away, the stranger, for this is a natural extension of the implicit love of the distant other, of the other-as-stranger – what Emmanuel Levinas has called "the infinity of the Other" – which is concealed in our friend, and which, in the words of Maurice Blanchot, puts us "authentically in relation" with him or her.

A Sensitivity Based Approach to Determining Non-Cooperative Solutions in Nash and Stackelberg Games

2012 ◽  
Author(s):  
Ehsan Ghotbi ◽  
Wilkistar A. Otieno ◽  
Anoop K. Dhingra
Keyword(s):  
Response Surface Methodology ◽  
Computational Effort ◽  
Stackelberg Games ◽  
Nash Solution ◽  
Numerical Errors ◽  
Multiobjective Problems ◽  
Cooperative Solutions ◽  
The One ◽  
Rational Reaction Set ◽  
The Nash Solution

A sensitivity based approach is presented to determine Nash solution(s) in multiobjective problems modeled as a non-cooperative game. The proposed approach provides an approximation to the rational reaction set (RRS) for each player. An intersection of these sets yields the Nash solution for the game. An alternate approach for generating the RRS based on design of experiments (DOE) combined with response surface methodology (RSM) is also explored. The two approaches for generating RRS are compared on three example problems to find Nash and Stackelberg solutions. It is seen that the proposed sensitivity based approach (i) requires less computational effort than a RSM-DOE approach, (ii) is less prone to numerical errors than the RSM-DOE approach, (iii) is able to find all Nash solutions when the Nash solution is not a singleton, (iv) is able to approximate non linear RRS, and (v) is able to find better a Nash solution on an example problem than the one reported in the literature.

scholarly journals Planet formation by pebble accretion in ringed disks

2020 ◽  
Vol 638 ◽  
pp. A1 ◽  
Author(s):  
A. Morbidelli
Keyword(s):  
Growth Rate ◽  
Upper Bound ◽  
Planet Formation ◽  
Accretion Rate ◽  
Central Star ◽  
Giant Planets ◽  
Type I ◽  
Dust Density ◽  
Dominant Process ◽  
The One

Context. Pebble accretion is expected to be the dominant process for the formation of massive solid planets, such as the cores of giant planets and super-Earths. So far, this process has been studied under the assumption that dust coagulates and drifts throughout the full protoplanetary disk. However, observations show that many disks are structured in rings that may be due to pressure maxima, preventing the global radial drift of the dust. Aims. We aim to study how the pebble-accretion paradigm changes if the dust is confined in a ring. Methods. Our approach is mostly analytic. We derived a formula that provides an upper bound to the growth of a planet as a function of time. We also numerically implemented the analytic formulæ to compute the growth of a planet located in a typical ring observed in the DSHARP survey, as well as in a putative ring rescaled at 5 AU. Results. Planet Type I migration is stopped in a ring, but not necessarily at its center. If the entropy-driven corotation torque is desaturated, the planet is located in a region with low dust density, which severely limits its accretion rate. If the planet is instead near the ring’s center, its accretion rate can be similar to the one it would have in a classic (ringless) disk of equivalent dust density. However, the growth rate of the planet is limited by the diffusion of dust in the ring, and the final planet mass is bounded by the total ring mass. The DSHARP rings are too far from the star to allow the formation of massive planets within the disk’s lifetime. However, a similar ring rescaled to 5 AU could lead to the formation of a planet incorporating the full ring mass in less than 1/2 My. Conclusions. The existence of rings may not be an obstacle to planet formation by pebble-accretion. However, for accretion to be effective, the resting position of the planet has to be relatively near the ring’s center, and the ring needs to be not too far from the central star. The formation of planets in rings can explain the existence of giant planets with core masses smaller than the so-called pebble isolation mass.

Hydrogen in Electrodynamics. VII The Pauli Principle

1991 ◽  
Vol 46 (10) ◽  
pp. 869-872 ◽  
Author(s):  
Hans Sallhofer
Keyword(s):  
Pauli Principle ◽  
Computational Effort ◽  
The One

AbstractAfter a discussion of the one-component Schrödinger (1926) and the four-component Dirac (1928) representation of hydrogen it is shown that the six-component electrodynamic picture turns out to be considerably simpler and clearer. The computational effort is reduced to a fraction.

Church-Rosser theorem for typed functional systems

1985 ◽  
Vol 50 (3) ◽  
pp. 782-790 ◽  
Author(s):  
George Koletsos
Keyword(s):  
Upper Bound ◽  
Type Structure ◽  
Functional Systems ◽  
Normalization Theorem ◽  
One Step ◽  
The One ◽  
Reduction Relation ◽  
The Church ◽  
The Way

Introduction. This paper contains a new proof of the Church-Rosser theorem for the typed λ-calculus, which also applies to systems with infinitely long terms.The ordinary proof of the Church-Rosser theorem for the general untyped calculus goes as follows (see [1]). If is the binary reduction relation between the terms we define the one-step reduction 1 in such a way that the following lemma is valid.Lemma. For all terms a and b we have: ab if and only if there is a sequence a = a0, …, an = b, n ≥ 0, such that aiiai + 1for 0 ≤ i < n.We then prove the Church-Rosser property for the relation 1 by induction on the length of the reductions. And by combining this result with the above lemma we obtain the Church-Rosser theorem for the relation .Unfortunately when we come to infinite terms the above lemma is not valid anymore. The difficulty is that, assuming the hypothesis for the infinitely many premises of the infinite rule, there may not exist an upper bound for the lengths n of the sequences ai = a0, …, an = bi (i < α); cf. the infinite rule (iv) in §6.A completely new idea in the case of the typed λ-calculus would be to exploit the type structure in the way Tait did in order to prove the normalization theorem. In this we succeed by defining a suitable predicate, the monovaluedness predicate, defined over the type structure and having some nice properties. The key notion permitting to define this predicate is the notion of I-form term (see below). This Tait-type proof has a merit, namely that it can be extended immediately to the case of infinite terms.

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