Reducing Fear of Crime for Sustaining Cities; A Case Study from Turkey.

In urban areas, fear of crime constitutes as much a problem as crime itself. Fear of crime is often associated with fear for oneââ¬â¢s personal safety, particularly, safety from violent crimes and physical or sexual harassment in public areas. The fear of crime and feelings of insecurity keeps people off the public places where crime or anti-social behaviour are likely to occur and also limits peopleââ¬â¢s behaviour to access to opportunities and facilities in their public environment. In other words, it creates a barrier to participation in the public life which reduces the liveability and sustainability of the city. It is obvious that, level of the fear of crime is unequally distributed considering the varied user profiles and places of cities. This paper is aimed to analyse how fear of crime is influenced by a variety of factors including actual crime rate, physical and social characteristics of the environment etc. with a specific case study from İzmir, Turkey in order to create safer and livable cities. Note: The alternative choice was to put this abstract under : ZW-SS 'Turkish cases in Contemporary issues/dimensions for regional development'

A Multiplier Related to Symmetric Stable Processes

In two recent papers [5] and [6], we generalized some classical results of Harmonic Analysis using probabilistic approach by means of a d- dimensional rotationally symmetric stable process. These results allow one to discuss some boundedness conditions with weaker hypotheses. In this paper, we study a multiplier theorem using these more general results. We consider a product process consisting of a d-dimensional symmetric stable process and a 1-dimensional Brownian motion, and use properties of jump processes to obtain bounds on jump terms and the L^p(R^d)-norm of a new operator.Comment: 13 page

Realization of affine type A Kirillov-Reshetikhin crystals via polytopes

On the polytope defined in Feigin, Fourier, and Littelmann (2011), associated to any rectangle highest weight, we define a structure of an type $A_n$-crystal. We show, by using the Stembridge axioms, that this crystal is isomorphic to the one obtained from Kashiwara's crystal bases theory. Further we define on this polytope a bijective map and show that this map satisfies the properties of a weak promotion operator. This implies in particular that we provide an explicit realization of Kirillov-Reshetikhin crystals for the affine type $A^{(1)}_n$ via polytopes

Extension of Mikhlin Multiplier Theorem to Fractional Derivatives and Stable Processes

In this paper, we prove a new generalized Mikhlin multiplier theorem whose conditions are given with respect to fractional derivatives in integral forms with two different integration intervals. We also discuss the connection between fractional derivatives and stable processes and prove a version of Mikhlin theorem under a condition given in terms of the infinitesimal generator of symmetric stable process. The classical Mikhlin theorem is shown to be a corollary of this new generalized version in this paper.Comment: 23 page

An Extension of a Boundedness Result for Singular Integral Operators

In this paper, we study some operators which are originated from classical Littlewood-Paley theory. We consider their modification with respect to our discontinuous setup, where the underlying process is the product of a one dimensional Brownian motion and a d-dimensional symmetric stable process. Two operators in focus are G-star and Area functionals. Using the results obtained in our previous paper, we show that these operators are bounded on L^p. Moreover, we generalise a classical multiplier theorem by weakening its conditions on the tail of the kernel of singular integrals.Comment: Minor corrections in the final versio