Additive Constant Research Articles

Induced subgraphs with large degrees at end-vertices for hamiltonicity of claw-free graphs

A graph is called \emph{claw-free} if it contains no induced subgraph isomorphic to $K_{1,3}$. Matthews and Sumner proved that a 2-connected claw-free graph $G$ is hamiltonian if every vertex of it has degree at least $(|V(G)|-2)/3$. At the workshop C\&C (Novy Smokovec, 1993), Broersma conjectured the degree condition of this result can be restricted only to end-vertices of induced copies of $N$ (the graph obtained from a triangle by adding three disjoint pendant edges). Fujisawa and Yamashita showed that the degree condition of Matthews and Sumner can be restricted only to end-vertices of induced copies of $Z_1$ (the graph obtained from a triangle by adding one pendant edge). Our main result in this paper is a characterization of all graphs $H$ such that a 2-connected claw-free graph $G$ is hamiltonian if each end-vertex of every induced copy of $H$ in $G$ has degree at least $|V(G)|/3+1$. This gives an affirmative solution of the conjecture of Broersma up to an additive constant.

Reply to “Comments on ‘MSE minus CAPE is the True Conserved Variable for an Adiabatically Lifted Parcel’”

Abstract A standard convention in moist thermodynamics, adopted by D. M. Romps and others, is to set the specific energy and entropy of dry air and liquid water to zero at the triple-point temperature and pressure. P. Marquet claims that this convention leads to physically incorrect results. To support this claim, Marquet presents numerical calculations of a lifted parcel. It is shown here that the claim is false and that the numerical calculations of Marquet are in error. In the context of a simple two-phase thermodynamic system, an analysis is presented here of the freedoms one has to choose additive constants in the definitions of energy and entropy. Many other misconceptions are corrected as well.

Better permutations for the single-processor scheduling with time restrictions

In this paper, we consider single-processor scheduling with time restrictions. Given a fixed integer $$B\ge 2$$ and a set of jobs, we need to schedule the jobs sequentially on a single processor subject to the following B-constraint. For any real x, no unit time interval $$[x, x+1)$$ is allowed to intersect more than B jobs. We show that there exists a permutation of the jobs which can be processed within a factor of $$\frac{5}{4}$$ of the optimum (plus an additional small constant) when $$B\ge 5$$ and this factor is best possible. When $$B=3, 4$$ , the corresponding factor equals $$\frac{B}{B-1}$$ . Furthermore, we present an asymptotically optimal permutation for $$B=2$$ . The results for $$B\ge 4$$ improve the previous work on this problem.

Certifying Equality With Limited Interaction

The equality problem is usually one's first encounter with communication complexity and is one of the most fundamental problems in the field. Although its deterministic and randomized communication complexity were settled decades ago, we find several new things to say about the problem by focusing on three subtle aspects. The first is to consider the expected communication cost (at a worst-case input) for a protocol that uses limited interaction--i.e., a bounded number of rounds of communication--and whose error probability is zero or close to it. The second is to treat the false negative error rate separately from the false positive error rate. The third is to consider the information cost of such protocols. We obtain asymptotically optimal rounds-versus-cost tradeoffs for equality: both expected communication complexity and information complexity scale as $$\Theta ({{\mathrm{ilog}}}^{r-1} n)$$ź(ilogr-1n), where r is the number of rounds and $${{\mathrm{ilog}}}^k n = \log \log \cdots \log n$$ilogkn=loglogźlogn, with k logs. These bounds hold even when the false negative rate approaches 1. For the case of zero-error communication cost, we obtain essentially matching bounds, up to a tiny additive constant. We also provide some applications. As an application of our information cost bounds, we obtain new bounded-round randomized lower bounds for the Intersection problem, in which there are two players who hold subsets $$S,T \subseteq [n]$$S,T⊆[n]. In many realistic scenarios, the sizes of S and T are significantly smaller than n, so we impose the constraint that $$|S|, |T| \le k$$|S|,|T|≤k. We study the minimum number of bits the parties need to communicate in order to compute the entire intersection set $$S \cap T$$SźT, using r rounds. We show that any r-round protocol has information cost (and thus communication cost) $$\Omega (k {{\mathrm{ilog}}}^r k)$$Ω(kilogrk) bits. We also give an O(r)-round protocol achieving $$O(k{{\mathrm{ilog}}}^r k)$$O(kilogrk) bits, which for $$r = \log ^* k$$r=logźk gives a protocol with O(k) bits of communication. This is in contrast to other basic problems such as computing the union or symmetric difference, for which $$\Omega (k\log (n/k))$$Ω(klog(n/k)) bits of communication is required for any number of rounds.

Unsteady vortex pattern in a flow over a flat plate at zero angle of attack (two-dimensional problem)

A technique of self-consistent analytical and numerical modeling of strongly and weakly (with the buoyancy frequency N = 1.2 and 0.02 s−1) stratified flows, as well as of almost and absolutely homogeneous flows (with N = 10−5 and 0.0 s−1), is developed using the fundamental system of equations without additional hypotheses or constants. Using an open-source software, the basic physical parameters (velocity, density, pressure) and their derivatives in the flow around a thick (0.5 cm) and a relatively thin (0.05 cm) rectangular plate 10 cm long are first calculated within the framework of a unique formulation over a wide range of velocities 0 < U < 80 cm/s. A complex flow structure comprising leading disturbances, internal waves, vortices, and thin interlayers is visualized. The maximal gradients are observed near the leading edge. In the unsteady vortex regime the structural parameters vary due to the nonlinear interaction of the flow components with different scales. For the finite plate, the calculated friction differs substantially from the Blasius solution but, for a semi-infinite plate, agrees to the accuracy of 5%.

LABORATORY TESTING OF LEICA AT401 LASER TRACKER

&lt;p&gt;This paper describes laboratory tests on a Leica AT401laser tracker. As the newer Leica AT402 model also uses the same firmware package, most of the results should also be valid for this device. First, we present the instrument’s firmware errors and the software used for testing. The ASME B89.4.19-2006 standard for testing laser trackers is briefly presented. The warm-up effect of the instrument is inspected with respect to both angle measurement and distance measurement. The absolute distance meter (ADM) is compared with a laboratory interferometer on a 30-meter long rail and also on a bench with automated movement of the carriage of the reflector. A time series of measurements for determining the additive constant is evaluated. A simple test of the stability of the distance measurement in field conditions is introduced. Most of the tests were carried out at the Research Institute of Geodesy, Topography and Cartography (RIGTC) and at the Faculty of Civil Engineering (FCE) of the Czech Technical University in Prague (CTU).&lt;/p&gt;

Femtosecond infrared spectroscopy of channelrhodopsin-1 chromophore isomerization.

Vibrational dynamics of the retinal all-trans to 13-cis photoisomerization in channelrhodopsin-1 from Chlamydomonas augustae (CaChR1) was investigated by femtosecond visible pump mid-IR probe spectroscopy. After photoexcitation, the transient infrared absorption of C-C stretching modes was detected. The formation of the 13-cis photoproduct marker band at 1193 cm−1 was observed within the time resolution of 0.3 ps. We estimated the photoisomerization yield to (60 ± 6) %. We found additional time constants of (0.55 ± 0.05) ps and (6 ± 1) ps, assigned to cooling, and cooling processes with a back-reaction pathway. An additional bleaching band demonstrates the ground-state heterogeneity of retinal.

A new method to break the mass-sheet degeneracy using aperture moments

Mass determinations from gravitational lensing shear and the higher order estimator flexion are both subject to the mass sheet degeneracy. Mass sheet degeneracy refers to a transformation that leaves the reduced shear and flexion invariant. In general, this transformation can be approximated by the addition of a constant surface mass density sheet. We propose a new technique to break the mass sheet degeneracy. The method uses mass moments of the shear or flexion fields in combination with convergence information derived from number counts which exploit the magnification bias. The difference between the measured mass moments provides an estimator for the magnitude of the additive constant that is the mass-sheet. For demonstrating this, we derive relations that hold true in general for n-th order moments and show how they can be employed effectively to break the degeneracy. We investigate the detectability of this degeneracy parameter from our method and find that the degeneracy parameter can be feasibly determined from stacked galaxy-galaxy lensing data and cluster lensing data. Furthermore, we compare the signal-to-noise ratios of convergence information from number counts with shear and flexion for SIS and NFW models. We find that the combination of shear and flexion performs best on galaxy and cluster scales and the convergence information can therefore be used to break the mass sheet degeneracy without quality loss in the mass reconstruction. In summary, there is power in the combination of shear, flexion, convergence and their higher order moments. With the anticipated wealth of lensing data from upcoming and future satellite missions - EUCLID and WFIRST - this technique will be feasible.

Holographic Ricci dark energy as running vacuum

Holographic Ricci dark energy (DE) that has been proposed ago has faced problems of future singularity. In the present work, we consider the Ricci DE with an additive constant in its density as running vacuum energy. We have analytically solved the Friedmann equations and also the role played by the general conservation law followed by the cosmic components together. We have shown that the running vacuum energy status of the Ricci DE helps to remove the possible future singularity in the model. The additive constant in the density of the running vacuum played an important role, such that, without that, the model predicts either eternal deceleration or eternal acceleration. But along with the additive constant, equivalent to a cosmological constant, the model predicts a late time acceleration in the expansion of the universe, and in the far future of the evolution it tends to de Sitter universe.

On the renormalization of operator products: the scalar gluonic case

In this paper we study the renormalization of the product of two operators $O_1=-\frac{1}{4} G^{\mu \nu}G_{\mu \nu}$ in QCD. An insertion of two such operators $O_1(x)O_1(0)$ into a Greens function produces divergent contact terms for $x\rightarrow 0$. In the course of the computation of the operator product expansion (OPE) of the correlator of two such operators $i\int\!\mathrm{d}^4x\,e^{iqx} T\{\,O_1(x)O_1(0)\}$ to three-loop order we discovered that divergent contact terms remain not only in the leading Wilson coefficient $C_0$, which is just the VEV of the correlator, but also in the Wilson coefficient $C_1$ in front of $O_1$. As this correlator plays an important role for example in QCD sum rules a full understanding of its renormalization is desireable. This work explains how the divergences encountered in higher orders of an OPE of this correlator should be absorbed in counterterms and derives an additive renormalization constant for $C_1$ from first principles and to all orders in perturnbation theory. The method to derive the renormalization of this operator product is an extension of the ideas of a paper by Spiridonov and can be generalized to other cases.

Saturation Numbers in Tripartite Graphs

AbstractGiven graphs H and F, a subgraph is an F‐saturated subgraph of H if , but for all . The saturation number of F in H, denoted , is the minimum number of edges in an F‐saturated subgraph of H. In this article, we study saturation numbers of tripartite graphs in tripartite graphs. For and n1, n2, and n3 sufficiently large, we determine and exactly and within an additive constant. We also include general constructions of ‐saturated subgraphs of with few edges for .

Graphs with Induced-Saturation Number Zero

Given graphs $G$ and $H$, $G$ is $H$-saturated if $H$ is not a subgraph of $G$, but for all $e \notin E(G)$, $H$ appears as a subgraph of $G + e$. While for every $n \ge |V(H)|$, there exists an $n$-vertex graph that is $H$-saturated, the same does not hold for induced subgraphs. That is, there exist graphs $H$ and values of $n \ge |V(H)|$, for which every $n$-vertex graph $G$ either contains $H$ as an induced subgraph, or there exists $e \notin E(G)$ such that $G + e$ does not contain $H$ as an induced subgraph. To circumvent this Martin and Smith make use of a generalized notion of "graph" when introducing the concept of induced saturation and the induced saturation number of graphs. This allows for edges that can be included or excluded when searching for an induced copy of $H$, and the induced saturation number is the minimum number of such edges that are required.In this paper, we show that the induced saturation number of many common graphs is zero. This yields graphs that are $H$-induced-saturated. That is, graphs such that no induced copy of $H$ exists, but adding or deleting any edge creates an induced copy of $H$. We introduce a new parameter for such graphs, indsat*($n;H$), which is the minimum number of edges in an $H$-induced-saturated graph. We provide bounds on indsat*($n;H$) for many graphs. In particular, we determine indsat*($n;H$) completely when $H$ is the paw graph $K_{1,3}+e$, and we determine indsat*(n;$K_{1,3}$) within an additive constant of four.

Transverse anisotropic magnetoresistance effects in pseudo-single-crystal γ′-Fe4N thin films

Transverse anisotropic magnetoresistance (AMR) effects, for which magnetization is rotated in an orthogonal plane to the current direction, were investigated at various temperatures, in order to clarify the structural transformation from a cubic to a tetragonal symmetry in a pseudo-single-crystal Fe4N film, which is predicted from the usual in-plane AMR measurements by the theory taking into account the spin-orbit interaction and crystal field splitting of 3d bands. According to a phenomenological theory of AMR, which derives only from the crystal symmetry, a cos 2θ component (C2tr) exists in transverse AMR curves for a tetragonal system but does not for a cubic system. In the Fe4N film, the C2tr shows a positive small value (0.12%) from 300 K to 50 K. However, the C2tr increases to negative value below 50 K and reaches to -2% at 5 K. The drastic increasing of the C2tr demonstrates the structural transformation from a cubic to a tetragonal symmetry below 50 K in the Fe4N film. In addition, the out-of-plane and in-plane lattice constants (c and a) were precisely determined with X-ray diffraction at room temperature using the Nelson-Riely function. As a result, the positive small C2tr above 50 K is attributed to a slightly distorted Fe4N lattice (c/a = 1.002).

Effective field theory of broken spatial diffeomorphisms

We study the low energy effective theory describing gravity with broken spatial diffeomorphism invariance. In the unitary gauge, the Goldstone bosons associated with broken diffeomorphisms are eaten and the graviton becomes a massive spin-2 particle with 5 well-behaved degrees of freedom. In this gauge, the most general theory is built with the lowest dimension operators invariant under only temporal diffeomorphisms. Imposing the additional shift and SO(3) internal symmetries, we analyze the perturbations on a FRW background. At linear perturbation level, the observables of this theory are characterized by five parameters, including the usual cosmological parameters and one additional coupling constant for the symmetry-breaking scalars. In the de Sitter and Minkowski limit, the three Goldstone bosons are supermassive and can be integrated out, leaving two massive tensor modes as the only propagating degrees of freedom. We discuss several examples relevant to theories of massive gravity.

Asymptotic entropic uncertainty relations

We analyze entropic uncertainty relations for two orthogonal measurements on a N-dimensional Hilbert space, performed in two generic bases. It is assumed that the unitary matrix U relating both bases is distributed according to the Haar measure on the unitary group. We provide lower bounds on the average Shannon entropy of probability distributions related to both measurements. The bounds are stronger than those obtained with use of the entropic uncertainty relation by Maassen and Uffink, and they are optimal up to additive constants. We also analyze the case of a large number of measurements and obtain strong entropic uncertainty relations, which hold with high probability with respect to the random choice of bases. The lower bounds we obtain are optimal up to additive constants and allow us to prove a conjecture by Wehner and Winter on the asymptotic behavior of constants in entropic uncertainty relations as the dimension tends to infinity. As a tool we develop estimates on the maximum operator norm of a submatrix of a fixed size of a random unitary matrix distributed according to the Haar measure, which are of independent interest.

Seismic response of reduced micropolar elastic half-space

This paper explores reduced micropolar theory to simulate ground motion during an earthquake. In this theory, rotational motions are kinematically independent of translational motions. Analytical expressions for ground displacement and rotational motions due to a buried seismic source are presented in this paper. This theory requires two additional material constants which characterise the microstructure of the medium compared with linear elastic theory. Ground motions are simulated for an earthquake of magnitude (M w) 5.0. The sensitivity of ground motion to these new material constants is reported. It is observed that rotations are sensitive to microstructure of the medium. A comparison with recorded rotations of the M w 5.2 Izu peninsula, Japan event is also presented in this article.

Relations between Linear ViscoElastic Behaviour of Bituminous Mixtures Containing Reclaimed Asphalt Pavement and Colloidal Structure of Corresponding Binder Blends

The paper presents an attempt to find a relation between Linear ViscoElastic (LVE) behaviour of bituminous mixtures containing Reclaimed Asphalt Pavement (RAP) and colloidal structure of corresponding binders. Three different base bitumens (15/25, 35/50 and 70/100 pen grade) were used to produce nine bituminous mixtures with varying RAP content (0%, 20%, 40% and 60%). Moreover, a 100% RAP mixture was produced (containing only RAP-extracted binder), for a total of ten mixtures. All mixtures have the same aggregates and grading curve. For each mixture, its corresponding binder blend was also produced, by perfectly mixing the base binder with RAP-extracted binder in the same proportions.Tension/Compression (T/C) complex modulus tests were performed on all mixtures, over a large range of frequencies (from 0.001Hz to 10Hz) and temperatures (from -25°C to 40°C). Experimental results were successfully fitted with the 2S2P1D (2 Springs, 2 Parabolic elements, 1 Dashpot) analogical model, developed at ENTPE. Therefore, for each mixture, a set of 7 model parameters and 2 additional constants (to take into account Time-Temperature Superposition Principle) was obtained. All binders were subjected to penetration tests and SARA (Saturates, Aromatics, Resins and Asphaltenes) fractioning, in order to have an indication on their colloidal structure. Colloidal Index (CI) of each binder was also calculated.Correlations between each parameter and all SARA fraction proportions, corresponding colloidal index values and penetrations are presented and analyzed.

A Study on the Cycle Life of Lithium-Ion Batteries Using In Situ 7Li Solid-State Nuclear Magnetic Resonance

The capacity fading of lithium ion batteries (LIBs) is investigated, using in situ 7Li solid-state nuclear magnetic resonance (NMR). LIB cells consisting of graphite or hard carbon and LiCoO2 are used and cycled under two different temperatures (10 and 25°C) and charge current rates (0.5 and 1 C). The cell capacity and the amount of Li stored in carbon are measured with a battery cycler and in situ 7Li solid-state NMR measurements before the beginning of the test and after every 100 test cycles. The in situ 7Li solid state NMRs provide sufficient information throughout the cycle tests to characterize all test conditions. The cell capacities are analyzed in terms of the 7Li NMR peak intensity, attributed to Li stored in carbon. This intensity shows affine proportionality with the cell capacity for every evaluation, with an additive constant that decreases with the increase in cell capacity fading. This may be related to the loss of Li storage caused by voltage “slippage.”

Determination of rate constants for trifluoromethyl radical addition to various alkenes via a practical method

A simple and practical method for the determination of rate constants for trifluoromethyl radical addition to various alkenes by applying competition kinetics is introduced. In the kinetic experiments the trifluoromethyl radicals are generated in situ from a commercially available hypervalent-iodine-CF3 reagent (Togni-reagent) by SET-reduction with TEMPONa in the presence of TEMPO and a π-acceptor. From the relative ratio of TEMPOCF3 and CF3-addition product formed, which is readily determined by (19)F-NMR spectroscopy, rate constants for trifluoromethyl radical addition to the π-acceptor can be calculated. The practical method is also applicable to measure rate constants for the addition of other perfluoroalkyl radicals to alkenes as documented for CF3CF2-radical addition reactions.

高レイノルズ数円管流れにおける管摩擦係数と流速分布

The mean velocity profile and the friction factor was measured at high Reynolds number using high Reynolds number actual flow facility (Hi-Reff) at NMIJ, AIST. The Reynolds number range of this experiment is from ReD=1.2×104 to 1.8×107. The Karman and additive constants of the mean velocity profile have the Reynolds number dependency for ReD<5.0×105 and they are constant for ReD>5.0×105. The Karman constants obtained from the velocity profile measurement and the friction factor measurement are completely consistent, which is 0.383, for ReD>5.0×105.