Dynamics of Electroweak Phase Transition in the 3-3-1-1 Model

The bubble nucleation in the framework of 3-3-1-1 model is studied. Previous studies show that first order electroweak phase transition occurs in two periods. In this paper we evaluate the bubble nucleation temperature throughout the parameter space. Using the stringent condition for bubble nucleation formation we find that in the first period, symmetry breaking from \(SU(3)\rightarrow SU(2)\), the bubble is formed at the nucleation temperature $T=150$ GeV and the lower bound of the scalar mass is 600 GeV. In the second period, symmetry breaking from \((SU(2)\rightarrow U(1)\), only subcritical bubbles are formed. This constraint eliminates the electroweak baryon genesis in the second period of the model.

Survival of Salmonella during Drying of Fresh Ginger Root (Zingiber officinale) and Storage of Ground Ginger

The survival of Salmonella on fresh ginger root (Zingiber officinale) during drying was examined using both a laboratory oven at 51 and 60°C with two different fan settings and a small commercially available food dehydrator. The survival of Salmonella in ground ginger stored at 25 and 37°C at 33% (low) and 97% (high) relative humidity (RH) was also examined. To inoculate ginger, a four-serovar cocktail of Salmonella was collected by harvesting agar lawn cells. For drying experiments, ginger slices (1 ± 0.5 mm thickness) were surface inoculated at a starting level of approximately 9 log CFU/g. Higher temperature (60°C) coupled with a slow fan speed (nonstringent condition) to promote a slower reduction in the water activity (aw) of the ginger resulted in a 3- to 4-log reduction in Salmonella populations in the first 4 to 6 h with an additional 2- to 3-log reduction by 24 h. Higher temperature with a higher fan speed (stringent condition) resulted in significantly less destruction of Salmonella throughout the 24-h period (P < 0.001). Survival appeared related to the rate of reduction in the aw. The aw also influenced Salmonella survival during storage of ground ginger. During storage at 97% RH, the maximum aw values were 0.85 at 25°C and 0.87 at 37°C; Salmonella was no longer detected after 25 and 5 days of storage, respectively, under these conditions. At 33% RH, the aw stabilized to approximately 0.35 at 25°C and 0.31 at 37°C. Salmonella levels remained relatively constant throughout the 365-day and 170-day storage periods for the respective temperatures. These results indicate a relationship between temperature and aw and the survival of Salmonella during both drying and storage of ginger.

Unified error bounds for all Newton–Cotes quadrature rules

It is well-known that the remaining term of a classical n-point Newton-Cotes quadrature depends on at least an n-order derivative of the integrand function. Discounting the fact that computing an n-order derivative requires a lot of differentiation for large n, the main problem is that an error bound for an n-point Newton-Cotes quadrature is only relevant for a function that is n times differentiable, a rather stringent condition. In this paper, by defining two specific linear kernels, we resolve this problem and obtain new error bounds for all closed and open types of Newton-Cotes quadrature rules. The advantage of the obtained bounds is that they do not depend on the norms of the integrand function and are very general such that they cover almost all existing results in the literature. Some illustrative examples are given in this direction.

Double Kernel Estimation of Sensitivities

In this paper we address the general issue of estimating the sensitivity of the expectation of a random variable with respect to a parameter characterizing its evolution. In finance, for example, the sensitivities of the price of a contingent claim are called the Greeks. A new way of estimating the Greeks has recently been introduced in Elie, Fermanian and Touzi (2007) through a randomization of the parameter of interest combined with nonparametric estimation techniques. In this paper we study another type of estimator that turns out to be closely related to the score function, which is well known to be the optimal Greek weight. This estimator relies on the use of two distinct kernel functions and the main interest of this paper is to provide its asymptotic properties. Under a slightly more stringent condition, its rate of convergence is the same as the one of the estimator introduced in Elie, Fermanian and Touzi (2007) and outperforms the finite differences estimator. In addition to the technical interest of the proofs, this result is very encouraging in the dynamic of creating new types of estimator for the sensitivities.

Double Kernel Estimation of Sensitivities

In this paper we address the general issue of estimating the sensitivity of the expectation of a random variable with respect to a parameter characterizing its evolution. In finance, for example, the sensitivities of the price of a contingent claim are called the Greeks. A new way of estimating the Greeks has recently been introduced in Elie, Fermanian and Touzi (2007) through a randomization of the parameter of interest combined with nonparametric estimation techniques. In this paper we study another type of estimator that turns out to be closely related to the score function, which is well known to be the optimal Greek weight. This estimator relies on the use of two distinct kernel functions and the main interest of this paper is to provide its asymptotic properties. Under a slightly more stringent condition, its rate of convergence is the same as the one of the estimator introduced in Elie, Fermanian and Touzi (2007) and outperforms the finite differences estimator. In addition to the technical interest of the proofs, this result is very encouraging in the dynamic of creating new types of estimator for the sensitivities.

MAPPING, PROGRAMMABILITY AND SCALABILITY OF PROBLEMS FOR QUANTUM SPEED-UP

This paper explores the reasons as to why the quantum paradigm is not so easy to extend to all of the classical computational algorithms. We also explain the failure of programmability and scalability in quantum speed-up. Due to the presence of quantum entropy, quantum algorithm cannot obviate the curse of dimensionality encountered in solving many complex numerical and optimization problems. Finally, the stringent condition that quantum computers have to be interaction-free, leave them with little versatility and practical utility.

A novel set of uncoordinated mutants inCaenorhabditis elegansuncovered by cold-sensitive mutations

A set of uncoordinated (Unc) cold-sensitive (cs) mutants was isolated at a stringent condition of 11 °C. About half of the 13 independently isolated cs-Unc mutants were alleles of three X-linked Unc mutants that exhibited the "kinker" phenotype. The remaining four isolates identified new mutants that exhibited "kinker," "coiler," or severe paralytic phenotypes. The temperature-sensitive period (TSP) for each gene was determined. As a homozygous or heterozygous dominant, unc-125 exhibited a TSP throughout all stages of development. Its severe paralysis was immediately observed upon a shift down to 11 °C and reversed upon a shift up to 23 °C. The reversible thermolability of the unc-125 gene product indicated that it may function in a multicomponent process involved in neuro-excitation. Key words : Caenorhabditis elegans, cold-sensitive uncoordinated mutants, cs-Unc.

Subgroups of SL2ℤ generated by elementary matrices

SynopsisAn elementary matrix has ones down the main diagonal and at most one element off the diagonal that differs from zero. We study the subgroups of SL2ℤ generated by sets of elementary matrices. Specifically, we give a stringent condition that the entries of a matrix belonging to such a group must satisfy.

Formal development of ordinal number theory

In this paper we shall develop a theory of ordinal numbers for the system ML, [6]. Since NF, [2], is a sub-system of ML one could let the ordinal arithmetic developed in [9] serve also as the ordinal arithmetic of ML. However, it was shown in [9] that the ordinal numbers of [9], NO, do not have all the usual properties of ordinal numbers and that theorems contradicting basic results of “intuitive ordinal arithmetic” can be proved.In particular it will be a theorem in our development of ordinal numbers that, for any ordinal number α, the set of all smaller ordinal numbers ordered by ≤ has ordinal number α; this result does not hold for the ordinals of [9] (see [9], XII.3.15). It will also be an easy consequence of our definition of ordinal number that proofs by induction over the ordinal numbers are permitted for arbitrary statements of ML; proofs by induction over NO can be carried through only for stratified statements with no unrestricted class variables.The class we shall take as the class of ordinal numbers, to be designated by ‘ORN’, will turn out to be a proper subclass of NO. This is because in ML there are two natural ways of defining the concept of well ordering. Sets which are well ordered in the sense of [9] we shall call weakly well ordered; sets which satisfy a certain more stringent condition will be called strongly well ordered. NO is the set of order types of weakly well ordered sets, while ORN is the class of order types of strongly well ordered sets. Basic properties of weakly and strongly well ordered sets are developed in Section 2.