Narrow Results

The notion of complex equiaffine manifolds is an affine generalization of Calabi–Yau manifolds. Similarly as in the Riemannian case the minimality of affine Lagrangian submanifolds in complex equiaffine spaces can be studied via calibrations, phase functions and variational formulas.

Uncertainty relations for the time-dependent singular oscillator in the number state and in the coherent state are investigated. We applied our developement to the Caldirola–Kanai oscillator perturbed by a singularity. For this system, the variation (Δx) decreased exponentially while (Δp) increased exponentially with time both in the number and in the coherent states. As k → 0 and χ → 0, the number state uncertainty relation in the ground state becomes 0.583216ℏ which is somewhat larger than that of the standard harmonic oscillator, ℏ/2. On the other hand, the uncertainty relation in all excited states become smaller than that of the standard harmonic oscillator with the same quantum number n. However, as k → ∞ and χ → 0, the uncertainty relations of the system approach the uncertainty relations of the standard harmonic oscillator, (n+1/2)ℏ.

The design of circuits which are robust against variations in operating and process conditions is crucial in today's IC industry. In the analog design flow this problem can be tackled during the sizing of a new circuit. However, hardly any methods are available which support the designer to compute such a robust design if discrete parameters should be considered in this design step. Discrete parameters arise predominantly if a layout-friendly sizing should be computed in the sense that, e.g., a manufacturing grid for the transistor lengths and widths is considered or that transistor multipliers are used to allow the layout of a transistor as multifinger or common centroid structure without applying rounding operations to the carefully computed sizing. This paper presents a new Branch-and-Bound based approach which allows the automatic computation of a robust design using classical and realistic worst case analysis. The results of the sizing of three circuits show that the new approach is highly efficient. The robustness of the results computed by the new approach is validated by Monte Carlo analyses.

We discuss the infinitesimal bending of curves and knots in ${{ℛ}}^3$. A brief overview of the results on the infinitesimal bending of curves is outlined. Change of the Willmore energy, as well as of the Möbius energy under infinitesimal bending of knots is considered. Our visualization tool devoted to visual representation of infinitesimal bending of knots is presented.

In the present paper, a one-dimensional continuous function of unbounded variation on the interval $[0,1]$ has been constructed. Box dimension of this function has been proved to be 1. Furthermore, Box dimension of its Riemann–Liouville fractional integral of any order has also been proved to be 1.

This paper mainly discusses the continuous functions whose fractal dimension is 1 on $[0,1]$. First, we classify continuous functions into unbounded variation and bounded variation. Then we prove that the fractal dimension of both continuous functions of bounded variation and their fractional integral is 1. As for continuous functions of unbounded variation, we solve several special types. Finally, we give the example of one-dimensional continuous function of unbounded variation.

In this paper, we make research on composition of continuous functions with Box dimension one of bounded variation or unbounded variation on $[0,1]$. It has been proved that one-dimensional continuous functions must be one of functions with bounded variation, or functions with finite unbounded variation points, or functions with infinite unbounded variation points on $[0,1]$. Based on discussion of one-dimensional continuous functions, fractal dimension, such as Box dimension, of Riemann–Liouville (R-L) fractional integral of those functions have been calculated. We get an important conclusion that Box dimension of R-L fractional integral of any one-dimensional continuous functions of any positive orders still is one. R-L fractional derivative of certain one-dimensional continuous functions has been explored elementary.

In this work, we consider fractal dimension such as Box dimension, of Weyl fractional integral of certain continuous functions. Upper Box dimension of Weyl fractional integral of continuous functions satisfying $\alpha$-order Hölder condition of positive order $v$ is no more than both $2-v$ and $2-\alpha$. Furthermore, it is no more than $2-\frac{v}{1-\alpha }$ which means strictly less than $2-v$. Meanwhile, $\alpha +v\ge 1$, Box dimension of Weyl fractional integral of continuous functions satisfying $\alpha$-order Hölder condition must be one.

In this paper, we mainly investigate relationship between fractal dimension of continuous functions and orders of Weyl fractional integrals. If a continuous function defined on a closed interval is of bounded variation, its Weyl fractional integral must still be a continuous function with bounded variation. Thus, both its Weyl fractional integral and itself have Box dimension one. If a continuous function satisfies Hölder condition, we give estimation of fractal dimension of its Weyl fractional integral. If a Hölder continuous function is equal to 0 on $ℝ/[a,b]$, a better estimation of fractal dimension can be obtained. When a function is continuous on $ℝ$ and its Weyl fractional integral is well defined, a general estimation of upper Box dimension of Weyl fractional integral of the function has been given which is strictly less than two. In the end, it has been proved that upper Box dimension of Weyl fractional integrals of continuous functions is no more than upper Box dimension of original functions.

In this paper, we mainly research on fractional differentiability of certain continuous functions with fractal dimension one. First, Riemann–Liouville fractional differential of differentiable functions must exist. Then, we prove the existence of Riemann–Liouville fractional differential of continuous functions satisfying the Lipschitz condition, which means that all of their Riemann–Liouville fractional integral of any positive orders in $(0,1)$ are differentiable. For continuous functions which do not satisfy the Lipschitz condition, we give counterexamples of certain continuous functions whose Riemann–Liouville fractional differential does not exist of certain positive order in $(0,1)$. Riemann–Liouville fractional differentiability of other one-dimensional continuous functions has also been investigated elementary. Fractional differentiability takes interpretation on physical problems like moving particle and transports through porous and percolation medium with residual memory.

In this paper, we mainly investigate continuous functions with unbounded variation on closed intervals. Given the increasing number of proposals and definitions of different kinds of functions with fractal structure in the scope of fractal functions, it is important to introduce a systematic classification and discuss elementary definitions of fractal functions. Different examples of fractal functions with certain fractal dimensions have been given. Then, we have introduced different kind of fractal function such as singular fractal function, irregular fractal function, regular fractal function and complete regular fractal function. We also introduce fractal functions of integer dimension with one and two, respectively. Other continuous and discontinuous functions with fractal structure have been given. Applications of fractal functions in interpolation, approximation and relationship between fractional calculus have been investigated. Finally, we studied fractal dimension spaces with different fractal dimensions.

In this paper, we have explored the local structure and fractal characteristics of fractal functions with certain fractal dimensions. The conclusion that points with inconsistent oscillation amplitudes with the upper Box dimension of the corresponding fractal functions have been proved to be nowhere dense. This will play an important supporting role in exploring the fractal dimension estimation of the combination of fractal functions.

In this paper, we research on the dimension preserving monotonous approximation by using fractal interpolation techniques. A constructive result of the approximating sequence of self-affine continuous functions has been given, which can converge to the object continuous function of bounded variation on $[0,1]$ monotonously and unanimously, meanwhile their graphs can be any value of the Hausdorff and the Box dimension between one and two. Further, such approximation for continuous functions of unbounded variation or even general continuous functions with non-integer fractal dimension has also been discussed elementarily.

Lift-gate is a rear closure system present in sports utility vehicles (SUV) and minivans. It has multiple design variables affecting multiple functional requirements. A wedge is a small piece of hardware used to stabilize the lift-gate especially in cross-car direction by providing the load path from the lift-gate to the surrounding structure. But, a wedge may increase the closing effort due to the reaction force in the swing direction. Furthermore, wedges need to accommodate the gap variation to bridge the lift-gate and the body frame. This paper presents the characteristics of two different types of wedges, their effects on the lift-gate system, and design methodologies to improve the wedge performance.

A 59-year-old man suffered from subcutaneous rupture of the flexor tendon of the little finger associated with fracture of the hook of hamate. He could not flex his little finger completely at the distal interphalangeal joint, but incomplete flexion of the proximal interphalangeal joint was possible. Surgical exploration revealed anomaly of the flexor digitorum superficialis of the little finger, as it originated from the palmar aspect of the carpal ligament, and a small portion of the muscle belly was traversed toward the A1 pulley over the profundus tendon and then it ran into the A1 pulley as a normal superficialis tendon.

The flexor digitorum superficialis of the little finger is well known to show variations, but our case is extremely rare, and furthermore there are no reports in the available literatures about the function of this anomalous muscle.

SINGAPORE – NUS Researchers Uncover Potent Parasite-killing Mechanism of Nobel Prize-Winning Anti-Malarial Drug.

SINGAPORE – Robotic Glove Invented by NUS Researchers Helps Patients Restore Hand Movements.

UNITED STATES – Study Reveals Environment, Behavior Contribute to Some 80 Percent of Cancers.

UNITED STATES – Probing the Mystery of How Cancer Cells Die.

UNITED STATES – Liver Hormone Works Through Brain's Reward Pathway to Reduce Preference for Sweets & Alcohol.

UNITED STATES – How Three Genes You've Never Heard of May Influence Human Fertility.

UNITED STATES – Researchers Find Link between Processed Foods and Autoimmune Diseases.

UNITED KINGDOM – Is Evolution More Intelligent Than We Thought?

UNITED KINGDOM – Unravelling the Genetics of Pregnancy and Heart Failure.

SWITZERLAND – New Global Framework to Eliminate Rabies.

CANADA – Droughts Hit Cereal Crops Harder Since 1980s.

TAIWAN – Discovery of Key Autophagy Terminator that Contributes to Cell Survival and Muscle Homeostasis.

Let $p\in (1,\infty )$, $\rho \in (2,\infty )$ and $W$ be a matrix $A_p$ weight. In this paper, we introduce a version of variation ${{𝒱}}_{\rho }({{{𝒯}}_n}_{,\ast })$ for matrix Calderón–Zygmund operators with modulus of continuity satisfying the Dini condition. We then obtain the $L^p(W)$-boundedness of ${{𝒱}}_{\rho }({{{𝒯}}_n}_{,\ast })$ with norm

The present article designed a genetic quadratic particle swarm optimization (GQPSO). Aiming at the low particle diversity at the early searching stage of quadratic particle swarm optimization (QPSO), the method adopts mutation and exchanging and regenerating mechanisms from genetic algorithm so as to avoid premature convergence and improves optimization. Meanwhile, the present article gave a comprehensive consideration to decision elements such as cost, resources, and service in the process of automotive parts' logistics, transportation, and loading; a model of automotive parts' logistics, transportation, and loading optimization was set up. GQPSO was introduced for solutions. Simulation examples show that GQPSO improves the computational efficiency, significantly, and there is a higher probability of searching the global optimum. It provides optimization method for the automobile parts' logistics and transportation plans.

In the present paper, the relation between invariants of the pseudo null curves and the variational vector fields of semi-Riemannian manifolds is introduced. After that, the Killing equations are written in terms of the Bishop curvatures along the pseudo null curve. By means of this approach, Killing equations make allow to interpret the movement of charged particles within the magnetic field. Afterwards, as an application, pseudo null magnetic curves are defined using the Killing variational vector field. The parametric representations of all pseudo null magnetic curves are determined in semi-Riemannian space form. Moreover, various examples of pseudo null magnetic curves are illustrated.

In [1], Shen Guangyu constructed several classes of new simple Lie algebras of characteristic 2, which are called the variations of G₂. In this paper, the authors investigate their derivation algebras. It is shown that G₂ and its variations all possess unique nondegenerate associative forms. The authors also find some nonsingular derivations of V_i G for i = 3, 4, 5, 6, and thereby construct some left-symmetric structures on V_i G for i = 3, 4, 5, 6. Some errors about the variations of in [1] are corrected.