Background The demand for health services in developing countries often outweighs provision. This article describes the present condition of physiotherapy in Bangladesh. Physiotherapy is not recognized as a profession by the government. There is no single registration and regulation body. The health-related and economic benefits of physiotherapy are not felt by the majority of Bangladeshi citiz...

For x = (x1, x2, · · · , xn) ∈ R+, the symmetric function φn(x, r) is defined by φn(x, r) = φn(x1, x2, · · · , xn; r) = ∏ 1≤i1<i2···<ir≤n  r ∑ j=1 1 + xij xij  , where r = 1, 2, · · · , n, and i1, i2, · · · , in are positive integers. In this article, the Schur convexity, Schur multiplicative convexity and Schur harmonic convexity of φn(x, r) are discussed. As applications, some inequalitie...

This paper describes a robust control design for automatic steering of passenger cars. Previous studies 1, 2] showed that reliable automatic driving at highway speed may not be achieved under practical conditions with look-down reference systems which use only one sensor at the front bumper to measure the lateral displacement of the vehicle from the lane reference. An additional lateral displac...

Let A be a subset of F p , the field of p elements with p prime. We let A + A = {a + b : a ∈ A, b ∈ A}, and AA = {ab : a ∈ A, b ∈ A}. It is fun (and useful) to prove lower bounds on max(|A+A|, |AA|) (see e.g. [BKT],[BGK],[G]). Recently, Garaev [G] showed that when |A| < p 1 2 one has the estimate max(|A + A|, |AA|) |A| 15 14. By using Plunneke's inequality in a slightly more sophisticated way, ...

We explore some geometric aspects of compensation compactness associated to Jacobian determinants. We provide the optimal constant in Wente's inequality-the original motivation of this work-and go on to give various extensions to geometric situations. In fact we improve Wente's inequality somewhat, making it more appropriate for applications in which optimal results are required. This is demons...

Problem 1: rewards from a small interval. Consider a version of the problem in which all the realized rewards are in the interval [12 , 1 2 + ] for some ∈ (0, 1 2). Define versions of UCB1 and Successive Elimination attain improved regret bounds (both logarithmic and root-T) that depend on the . Hint: Use a more efficient version of Hoeffding Inequality in the slides from the first lecture. It ...

IfH is a Hopf algebra whose square of the antipode is the identity, v ∈ L(V )⊗H is a corepresentation, and π : H → L(W ) is a representation, then u = (id ⊗ π)v satisfies the equation (t ⊗ id)u = ((t ⊗ id)u) of the vertex models for subfactors. A universal construction shows that any solution u of this equation arises in this way. A more elaborate construction shows that there exists a “minimal...

is a pseudo-effective divisor on Y . We have an application to a problem concerning the positivity of divisors on the moduli space of stable curves, namely, let Mg (resp. Mg) be the moduli space of stable (resp. smooth) curves of genus g ≥ 2. Let λ be the Hodge class and δi’s (i = 0, . . . , [g/2]) are boundary classes. Then, a divisor (8g+4)λ− gδ0− ∑[g/2] i=1 4i(g− i)δi is pseudo-effective, an...

In this paper, we study the agent’s optimal quitting in a continuous-time principal-agent problem, where the agent is payed once at the end of the contract. In a jump diffusion setting, we formulate the agency problem as a combined optimal stopping and stochastic control problem in weak formulation. To find the solutions, we develop the classical verification theorem in terms of Variational Ine...

This book, first published in the United States in *939, has now been published in Great Britain. It is very readable and delightfully illustrated with 29 drawings and paintings. Mrs. Wickes is a Jungian analyst and her book Provides an excellent introduction to analytical Psychology and is based on case material collected ?ver years of practice. In the first section Jungian concepts are explai...