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INTRODUCTION
The prostate cancer is difficult to predict, and treatment failure is associated with local infiltration, as well as distant metastases. Adhesion and migration abilities to of cancer cells play a major role in formation of metastasis. The participation of β-catenin in pathogene-sis of many types of cancer and benign processes has been an… (More)

Carcinoma of the prostate gland is the most common neoplasm in men. Its treatment depends on multiple factors among which local staging plays a significant role. The basic method is transrectal ultrasound imaging. This examination enables imaging of the prostate gland and its abnormalities, but it also allows ultrasound-guided biopsies to be conducted. A… (More)

A tissue thermal conductivity (Ks) is an important parameter which knowledge is essential whenever thermal fields induced in selected organs are predicted. The main objective of this study was to develop an alternative ultrasonic method for determining Ks of tissues in vitro suitable for living tissues. First, the method involves measuring of… (More)

The issue of maximizing penetration depth with concurrent retaining or enhancement of image resolution constitutes one of the time invariant challenges in ultrasound imaging. Concerns about potential and undesirable side effects set limits on the possibility of overcoming the frequency dependent attenuation effects by increasing peak acoustic amplitudes of… (More)

Factorial function and binomial symbol play important role in contemporary mathematics. In this paper we explore the generalized binomial symbol and show some of its properties. We remind the definition of β −sequences and we prove that some well known sequences are β −sequences. Finally we show how some of the enclosed here examples can be done with the… (More)

The following full text is a preprint version which may differ from the publisher's version. Abstract Let k[X] be the algebra of polynomials in n variables over a field k of characteristic zero, and let f ∈ k[X] k. We present a construction of a derivation d of k[X] whose ring of constants is equal to the integral closure of k[f ] in k[X]. A similar… (More)

For centuries tissue palpation has been an important diagnostic tool. During palpation, tumors are felt as tissues harder than the surrounding tissues. The significance of palpation is related to the relationship between mechanical properties of different tissue lesions. The assessment of tissue stiffness through palpation is based on the fact that… (More)

- Arno van den Essen, Andrzej Nowicki, Andrzej Tyc
- 2016

The version of the following full text has not yet been defined or was untraceable and may differ from the publisher's version.

- Andrzej Nowicki
- 2014

Let R be an integral domain in which every two nonzero elements have a greatest common divisor. Let (a n) n1 be a sequence of nonzero elements in R. We prove that gcd(a n , a m) = a gcd(n,m) for all n, m 1 if and only if a n = d|n c d for n 1, where c 1 = a 1 and c n = lcm(a 1 , a 2 ,. .. , a n)/lcm(a 1 , a 2 ,. .. , a n−1) for n 2. We also present some… (More)