Sequence Whenever Research Articles

Seismic signature of electron degeneracy in the core of red giants: Hints for mass transfer between close red-giant companions

The detection of mixed modes in red giants with space missions COROT and Kepler has revealed their deep internal structure. These modes allow us to characterize the pattern of pressure modes (through the measurement of their asymptotic frequency separation Δν) and the pattern of gravity modes (through the determination of their asymptotic period spacing ΔΠ1). It has been shown that red giant branch (RGB) stars regroup on a well-defined sequence in the Δν − ΔΠ1 plane. Our first goal is to theoretically explain the features of this sequence and understand how it can be used to probe the interiors of red giants. Using a grid of red giant models computed with MESA, we demonstrate that red giants join the Δν − ΔΠ1 sequence whenever electron degeneracy becomes strong in the core. We argue that this can be used to estimate the central densities of these stars, and potentially to measure the amount of core overshooting during the main sequence part of the evolution. We also investigate a puzzling subsample of red giants that are located below the RGB sequence, in contradiction with stellar evolution models. After checking the measurements of the asymptotic period spacing for these stars, we show that they are mainly intermediate-mass red giants. This is doubly peculiar because these stars should have nondegenerate cores and they are expected to be located well above the RGB sequence. We show that these peculiarities are well accounted for if these stars result from the interaction between two low-mass (M ≲ 2 M⊙) close companions during the red giant branch phase. If the secondary component has already developed a degenerate core before mass transfer begins, it becomes an intermediate-mass giant with a degenerate core. The secondary star is then located below the degenerate sequence, which is in agreement with the observations.

Approximation of Modified Baskakov Operators Based on Parameter s

In this article, we define and study a family of modified Baskakov type operators based on a parameter . This family is a generalization of the classical Baskakov sequence. First, we prove that it converges to the function being approximated. Then, we find a Voronovsky-type formula and obtain that the order of approximation of this family is . This order is better than the order of the classical Baskakov sequence whenever . Finally, we apply our sequence to approximate two test functions and analyze the numerical results obtained.

Linking in infinite dimensional spaces using the Leray-Schauder index

Many problems arising in science and engineering call for the solving of the Euler-Lagrange equations of functionals. Thus, solving the Euler-Lagrange equations is tantamount to finding critical points of the corresponding functional. An idea that has been very successful is to find appropriate sets that separate the functional. This method is called linking. Two sets A,B are said to separate a functional G if the supremum of G on A is less than or equal to the infimum of G on B. Two sets of the space are said to link if they produce a critical sequence whenever they separate a functional. If the critical sequence has a convergent sub-sequence, then that produces a critical point. Finding sets that separate a functional is quite easy, but determining whether or not the sets link is quite another story. It appears that the only way we can check to see if two sets link, is to require that one of them be contained in a finite-dimensional subspace. The reason is that in order to verify the definition, we need to invoke the Brouwer fixed point theorem. Our aim is to find a counterpart of linking that holds true when both sets are infinite dimensional. We adjust our definitions to accommodate infinite dimensions. These definitions reduced to the usual definitions when one set is finite dimensional. In order to prove the corresponding theorems, we make adjustments to the topology of the space and introduce infinite dimensional splitting. This allows us to use a form of compactness on infinite dimensional subspaces which does not exist under the usual topology. We lose the Brouwer index, but we are able to replace it with the Leray-Schauder index. We carry out the details in Sections 5 and 6. In Section 7 we solve a system of equations which require infinite dimensional splitting.

A mathematical analysis of fairness in shootouts

Abstract A shootout is a popular mechanism to identify a winner of a match between two teams. It consists of rounds in which each team gets, sequentially, an opportunity to score a point. It has been shown empirically that shooting first or shooting second in a round has an impact on the scoring probability. This raises a fairness question: is it possible to specify a sequence such that identical teams have equal chance of winning? We show that, for a sudden death, no repetitive sequence can be fair. In addition, we show that the so-called Prohuet–Thue–Morse sequence is not fair. There is, however, an algorithm that outputs a fair sequence whenever one exists. We also analyze the popular best-of-$k$ shootouts and show that no fair sequence exists in this situation. In addition, we find explicit expressions for the degree of unfairness in a best-of-$k$ shootout; this allows sports administrators to asses the effect of the length of the shootout on the degree of unfairness.

A variation on strongly lacunary delta ward continuity in 2-normed spaces

A sequence $(x_{k})$ of points in a subset E of a 2-normed space $X$ is called strongly lacunary $\delta$-quasi-Cauchy, or $N_\theta$-$\delta$-quasi-Cauchy if $(\Delta x_k)$ is $N_\theta$-convergent to 0, that is $\lim_{r\rightarrow\infty}\frac{1}{h_r}\sum_{k\in I_r}||\Delta^2 x_k, z||=0$ for every fixed $z\in X$. A function defined on a subset $E$ of $X$ is called strongly lacunary $\delta$-ward continuous if it preserves $N_{\theta}$-$\delta$-quasi-Cauchy sequences, i.e. $(f(x_{k}))$ is an $N_{\theta}$-$\delta$-quasi-Cauchy sequence whenever $(x_{k})$ is. In this study we obtain some theorems related to strongly lacunary $\delta$-quasi-Cauchy sequences.

Synthetic Inducible Regulatory Systems Optimized for the Modulation of Secondary Metabolite Production in Streptomyces.

Biosynthesis of secondary metabolites is a highly complex process that often requires tight control of their production, as overproduction of metabolites could be toxic and also may cause metabolic burden to their hosts. Tight control of metabolite production could be achieved by expressing key biosynthetic genes under control of an inducible regulatory system. In this study, we employed the modular design approach to build a high performance synthetic inducible regulatory system that displays a large dynamic range and thus is well-suited for the modulation of secondary metabolite production in Streptomyces. To this end, an inducible regulatory system was divided into three separate functional modules: (1) the induction module, (2) the target expression module, and (3) the repressor expression module. Then, these three separate modules were individually optimized in a stepwise manner and assembled to a new system. First, the cumate (CMT) induction module was chosen as the best performing induction module based on the large dynamic range and moderate inducer sensitivity. Then the CMT induction module maintained its performance when combined with diverse constitutive target expression modules, in which overall dynamic ranges varied depending on maximum promoter strengths. Lastly, the repressor expression module was optimized to achieve complete elimination of leaky expression, further increasing the dynamic range of the system. We also demonstrate that any strong constitutive regulatory system could be converted into an inducible regulatory system by simple CRISPR/Cas9-aided markerless insertion of an operator sequence whenever tight control of gene expression is required. We believe that the synthetic inducible regulatory system we report here would become a useful tool in modulating secondary metabolite production in Streptomyces.

İstatistiksel boşluklu delta 2 quasi Cauchy dizileri

The notion of a lacunary statistical d 2 -quasi-Cauchyness of sequence of real numbers is introduce and investigated. In this work, we present interesting theorems related to lacunary statistically d 2 -ward continuity. A function f, whose domain is included in R, and whose range included in R is called lacunary statistical d 2 ward continuous if it preserves lacunary statistical d 2 quasi-Cauchy sequences, i.e. (f(x k )) is a lacunary statistically d 2 quasi-Cauchy sequence whenever (x k ) is a lacunary statistically d 2 quasi-Cauchy sequence, where a sequence (x k ) is called lacunary statistically d 2 quasi-Cauchy if ( D 2 x k ) is a lacunary statistically quasi-Cauchy sequence. We find out that the set of lacunary statistical d 2 ward continuous functions is closed as a subset of the set of continuous functions.

A variation on lacunary statistical quasi cauchy sequences

In this paper, the concept of a lacunary statistically -quasi-Cauchysequence is investigated. In this investigation, we proved interesting theoremsrelated to lacunary statisticallycontinuities. A real valued function f de…ned on a subset A of R, the set ofreal numbers, is called lacunary statisticallyserves lacunary statistically delta quasi-Cauchy sequences of points in A, i.e.(f (k))is a lacunary statistically delta quasi-Cauchy sequence whenever (k)is a lacunary statistically delta quasi-Cauchy sequence of points in A, wherea sequence (k)is called lacunary statistically delta quasi-Cauchy if (a lacunary statistically quasi-Cauchy sequence. It turns out that the set oflacunary statisticallyof continuous functions

Dynamic resequencing at mixed-model assembly lines

In this paper, we investigate a dynamic resequencing problem covering realistic properties of a mixed-model assembly line. To this end, we present a mathematical model that addresses dynamically supplied blocking information and viable due dates. We developed two different strategies that use a static resequencing algorithm as a subroutine. One strategy integrates each unblocked order immediately into the planned sequence, whereas the other strategy waits for good positions that do not conflict with the due dates. All algorithms construct guaranteed feasible sequences. Using industrial test data, we show that both strategies perform significantly better than a simple method derived from practice. A replanning procedure that tries to improve the current planned sequence whenever computing time suffices yields an additional improvement for both strategies.

Strongly lacunary ward continuity in 2-normed spaces.

A function f defined on a subset E of a 2-normed space X is strongly lacunary ward continuous if it preserves strongly lacunary quasi-Cauchy sequences of points in E; that is, (f(x k)) is a strongly lacunary quasi-Cauchy sequence whenever (x k) is strongly lacunary quasi-Cauchy. In this paper, not only strongly lacunary ward continuity, but also some other kinds of continuities are investigated in 2-normed spaces.

Nθ‐Ward Continuity

A function f is continuous if and only if f preserves convergent sequences; that is, (f(αn)) is a convergent sequence whenever (αn) is convergent. The concept of Nθ‐ward continuity is defined in the sense that a function f is Nθ‐ward continuous if it preserves Nθ‐quasi‐Cauchy sequences; that is, (f(αn)) is an Nθ‐quasi‐Cauchy sequence whenever (αn) is Nθ‐quasi‐Cauchy. A sequence (αk) of points in R, the set of real numbers, is Nθ‐quasi‐Cauchy if , where Δαk = αk+1 − αk, Ir = (kr−1, kr], and θ = (kr) is a lacunary sequence, that is, an increasing sequence of positive integers such that k0 = 0 and hr : kr − kr−1 → ∞. A new type compactness, namely, Nθ‐ward compactness, is also, defined and some new results related to this kind of compactness are obtained.

Slowly Oscillating Continuity

A function f is continuous if and only if, for each point x0 in the domain, lim⁡n→∞f(xn) = f(x0), whenever lim⁡n→∞xn = x0. This is equivalent to the statement that (f(xn)) is a convergent sequence whenever (xn) is convergent. The concept of slowly oscillating continuity is defined in the sense that a function f is slowly oscillating continuous if it transforms slowly oscillating sequences to slowly oscillating sequences, that is, (f(xn)) is slowly oscillating whenever (xn) is slowly oscillating. A sequence (xn) of points in R is slowly oscillating if , where [λn] denotes the integer part of λn. Using ɛ > 0′s and δ′s, this is equivalent to the case when, for any given ɛ > 0, there exist δ = δ(ɛ) > 0 and N = N(ɛ) such that |xm − xn| < ɛ if n ≥ N(ɛ) and n ≤ m ≤ (1 + δ)n. A new type compactness is also defined and some new results related to compactness are obtained.

A sound and complete algorithm for distributed commerce transactions

In a multi-party transaction (also called a distributed commerce transaction) agents face risks from dealing with untrusted agents. These risks are compounded in the face of deadlines, e.g., an agent may fail to deliver purchased goods by the time the goods are needed. We characterize the risks, and present a distributed algorithm that mitigates these risks, by using pairwise exchanges and trusted intermediaries. The algorithm generates a safe sequence of actions that completes a commerce transaction without risk, if such a sequence exists. We show that the algorithm is sound (produces only safe multi-agent action sequences) and complete (finds a safe sequence whenever one exists). The initial restriction of guaranteeing safety even when none of the principals trusts another can be relaxed in some cases, so we show how to handle principals that do trust each other and interact directly rather than through a trusted intermediary.

Adaptive quadtree coding of motion-compensated image sequences for use on the broadband ISDN

An image-coding technique is described in which an adaptive quadtree scheme is used to encode motion-compensated difference images. A mechanism is determined within the encoding process that allows a predetermined level of image quality to be selected by the user at call setup time and then maintained by the encoder. The coder operates in a variable-bit-rate mode providing a video service of near-constant image quality. A multilayered version of the coding scheme is also described in which the degradation caused by cell loss during transmission can be limited in its effect and removed completely within a short period of time. The recovery from cell loss is achieved by sending blocks from the original image sequence whenever cells are known to have been deleted by the local-network access node. >

Pollaczek polynomials and summability methods

It is shown that a (suitably normalized) Pollaczek polynomial P λ n ( x; a, b) is a regular transformation of a convergent sequence whenever x ϵ R 3⧹[−1.1]. This immediately leads to an asymptotic formula.

Effects of a stochastic initial mass function on the upper main sequence band

The theoretical (Mb versus Log Te) HR diagram for the brightest galactic OB stars shows an upper boundary for the luminosity, which is characterized by a decreasing luminosity with decreasing effective temperature (Humphreys and Davidson, 1979). The existence of this limit was interpreted by Chiosi et al. (1978) as due to the effect of mass loss by stellar wind on the evolution of most massive stars in core H-burning phase. In fact, evolutionary models calculated at constant mass cover a wider and wider range in effective temperature as the initial mass increases during the main sequence phase. On the contrary, sufficiently high mass-loss rates make the evolutionary sequences of most massive stars (M 60⩾Mʘ) shrink toward the zero age main sequence whenever, due to mass loss, CNO processed material is brought to the surface (Chiosi et al., 1978; de Loore et al., 1978; Maeder, 1980).