On the Rate of Convergence of Two Bernstein–Bézier Type Operators for Bounded Variation Functions, II

AbstractThe rates of convergence of two Bernstein–Bézier type operators B(α)n and L(α)n for functions of bounded variation have been studied for the case α⩾1 by the author and A. Piriou (1998, J. Approx. Theory95, 369–387). In this paper the other case 0<α<1 is treated and asymptotically optimal estimations of B(α)n and L(α)n for functions of bounded variation are obtained. Besides, some interesting behaviors of the operators B(α)n and L(α)n (α>0) for monotone functions and functions of bounded variation are also given

Approximation for absolutely continuous functions by Stancu Beta operators

In this paper, we obtain an exact estimate for the first-order absolute moment of Stancu Beta operators by means of the Stirling formula and integral operations. Then we use this estimate for establishing a theorem on approximation of absolutely continuous functions by Stancu Beta operators.Отримано точну оцiнку для абсолютного моменту бета-операторiв Станку першого порядку iз використанням формули Стiрлiнга та iнтегральних операцiй. Цю оцiнку використано для встановлення теореми про наближення абсолютно неперервних функцiй бета-операторами Станку

Holographic thermalization with a chemical potential in Gauss-Bonnet gravity

Holographic thermalization is studied in the framework of Einstein-Maxwell-Gauss-Bonnet gravity. We use the two-point correlation function and expectation value of Wilson loop, which are dual to the renormalized geodesic length and minimal area surface in the bulk, to probe the thermalization. The numeric result shows that larger the Gauss-Bonnet coefficient is, shorter the thermalization time is, and larger the charge is, longer the thermalization time is, which implies that the Gauss-Bonnet coefficient can accelerate the thermalization while the charge has an opposite effect. In addition, we obtain the functions with respect to the thermalization time for both the thermalization probes at a fixed charge and Gauss-Bonnet coefficient, and on the basis of these functions, we obtain the thermalization velocity, which shows that the thermalization process is non-monotonic. At the middle and later periods of the thermalization process, we find that there is a phase transition point, which divides the thermalization into an acceleration phase and a deceleration phase. We also study the effect of the charge and Gauss-Bonnet coefficient on the phase transition point.Comment: 23 pages, many figures,footnote 4 is modified. arXiv admin note: substantial text overlap with arXiv:1305.484

Holographic thermalization in noncommutative geometry

Gravitational collapse of a shell of dust in noncommutative geometry is probed by the renormalized geodesic length, which is dual to probe the thermalization by the two-point correlation function in the dual conformal field theory. We find that larger the noncommutative parameter is, longer the thermalization time is, which implies that the large noncommutative parameter delays the thermalization process. We also investigate how the noncommutative parameter affects the thermalization velocity and thermalization acceleration.Comment: some materials have been delete

Van der Waals-like phase transition from holographic entanglement entropy in Lorentz breaking massive gravity

In this paper, phase transition of AdS black holes in lorentz breaking massive gravity has been studied in the framework of holography. We find that there is a first order phase transition(FPT) and second order phase transition(SPT) both in Bekenstein-Hawking entropy(BHE)-temperature plane and holographic entanglement entropy(HEE)-temperature plane. Furthermore, for the FPT, the equal area law is checked and for the SPT, the critical exponent of the heat capacity is also computed. Our results confirm that the phase structure of HEE is similar to that of BHE in lorentz breaking massive gravity, which implies that HEE and BHE have some potential underlying relationship.Comment: 10 pages, 10 figure

Mutual correlation in the shock wave geometry

We probe the shock wave geometry with the mutual correlation in a spherically symmetric Reissner Nordstr\"om AdS black hole on the basis of the gauge/gravity duality. In the static background, we find that the regions living on the boundary of the AdS black holes are correlated provided the considered regions on the boundary are large enough. We also investigate the effect of the charge on the mutual correlation and find that the bigger the value of the charge is, the smaller the value of the mutual correlation will to be. As a small perturbation is added at the AdS boundary, the horizon shifts and a dynamical shock wave geometry forms after long time enough. In this dynamic background, we find that the greater the shift of the horizon is, the smaller the mutual correlation will to be. Especially for the case that the shift is large enough, the mutual correlation vanishes, which implies that the considered regions on the boundary are uncorrelated. The effect of the charge on the mutual correlation in this dynamic background is found to be the same as that in the static background.Comment: 10 page

Species-specific Differences among KCNMB3 BK β3 Auxiliary Subunits: Some β3 N-terminal Variants May Be Primate-specific Subunits

The KCNMB3 gene encodes one of a family of four auxiliary β subunits found in the mammalian genome that associate with Slo1 α subunits and regulate BK channel function. In humans, the KCNMB3 gene contains four N-terminal alternative exons that produce four functionally distinct β3 subunits, β3a–d. Three variants, β3a–c, exhibit kinetically distinct inactivation behaviors. Since investigation of the physiological roles of BK auxiliary subunits will depend on studies in rodents, here we have determined the identity and functional properties of mouse β3 variants. Whereas β1, β2, and β4 subunits exhibit 83.2%, 95.3%, and 93.8% identity between mouse and human, the mouse β3 subunit, excluding N-terminal splice variants, shares only 62.8% amino acid identity with its human counterpart. Based on an examination of the mouse genome and screening of mouse cDNA libraries, here we have identified only two N-terminal candidates, β3a and β3b, of the four found in humans. Both human and mouse β3a subunits produce a characteristic use-dependent inactivation. Surprisingly, whereas the hβ3b exhibits rapid inactivation, the putative mβ3b does not inactivate. Furthermore, unlike hβ3, the mβ3 subunit, irrespective of the N terminus, mediates a shift in gating to more negative potentials at a given Ca2+ concentration. The shift in gating gradually is lost following patch excision, suggesting that the gating shift involves some regulatory process dependent on the cytosolic milieu. Examination of additional genomes to assess conservation among splice variants suggests that the putative mβ3b N terminus may not be a true orthologue of the hβ3b N terminus and that both β3c and β3d appear likely to be primate-specific N-terminal variants. These results have three key implications: first, functional properties of homologous β3 subunits may differ among mammalian species; second, the specific physiological roles of homologous β3 subunits may differ among mammalian species; and, third, some β3 variants may be primate-specific ion channel subunits

Miniaturization of Branch-Line Coupler Using Composite Right/Left-Handed Transmission Lines with Novel Meander-shaped-slots CSSRR

A novel compact-size branch-line coupler using composite right/left-handed transmission lines is proposed in this paper. In order to obtain miniaturization, composite right/left-handed transmission lines with novel complementary split single ring resonators which are realized by loading a pair of meander-shaped-slots in the split of the ring are designed. This novel coupler occupies only 22.8% of the area of the conventional approach at 0.7 GHz. The proposed coupler can be implemented by using the standard printed-circuit-board etching processes without any implementation of lumped elements and via-holes, making it very useful for wireless communication systems. The agreement between measured and stimulated results validates the feasible configuration of the proposed coupler