On a remarkable semigroup of homomorphisms with respect to free multiplicative convolution

Let M denote the space of Borel probability measures on the real line. For every nonnegative t we consider the transformation $\mathbb B_t : M \to M$ defined for any given element in M by taking succesively the the (1+t) power with respect to free additive convolution and then the 1/(1+t) power with respect to Boolean convolution of the given element. We show that the family of maps {\mathbb B_t|t\geq 0} is a semigroup with respect to the operation of composition and that, quite surprisingly, every $\mathbb B_t$ is a homomorphism for the operation of free multiplicative convolution. We prove that for t=1 the transformation $\mathbb B_1$ coincides with the canonical bijection $\mathbb B : M \to M_{inf-div}$ discovered by Bercovici and Pata in their study of the relations between infinite divisibility in free and in Boolean probability. Here M_{inf-div} stands for the set of probability distributions in M which are infinitely divisible with respect to free additive convolution. As a consequence, we have that $\mathbb B_t(\mu)$ is infinitely divisible with respect to free additive convolution for any for every $\mu$ in M and every t greater than or equal to one. On the other hand we put into evidence a relation between the transformations $\mathbb B_t$ and the free Brownian motion; indeed, Theorem 4 of the paper gives an interpretation of the transformations $\mathbb B_t$ as a way of re-casting the free Brownian motion, where the resulting process becomes multiplicative with respect to free multiplicative convolution, and always reaches infinite divisibility with respect to free additive convolution by the time t=1.Comment: 30 pages, minor changes; to appear in Indiana University Mathematics Journa

Argument, Determing Factor in Trade Negotiations

The paper presents pragmatic guidance on current trends, the argument is a set of techniques that highlight the benefits they offer is a negotiator for the needs of others. The study focuses on rational arguments, by evidence and demonstration and practice of negotiations develop, characterized by a constant interaction of the elements which contribute to the possibilities offered to both partners. It stresses that the success of negotiations is determined by the negotiator's ability to define the steps, strategies, plan and ways of reasoning argument. Given that negotiations can occur during many different points of view, the paper presents techniques of counter-arguments and factors that may influence the success during the argument. The study highlights the fact that a negotiator can control the power dynamics of a negotiation of power through the use of traditional elements such as control of resources, time or information.trade negotiations, control resources.

PRIORITY MANAGEMENT – A DIRECTION TOWARDS COMPETITIVENESS

In a time when the most of us have to cope with globalization, the key for surpassing the negative effects produced by it, resides in choosing the right strategy. This necessary involves a performance management. Through this paper we propose priority management as an efficient way of thinking about gaining the vital competitive advantage.priority management, the Pareto law, 1-3-6 method, competitiveness, efficiency

COMPETITIVE INTELLIGENCE

There are many challenges to face in this century. It’s an era of information. Those who have the best information are going to win the race for supremacy on the market. More and more managers are aware of the fact that they have to do something to remain on the market and to be successful. They have to adapt and to try to gain an advantage over the competitors. Nowadays, the only thing that makes the difference is the company’s competitiveness. The times when the one who had the capacity to produce more was the leader are long gone; now all the actors on every market are focused on quality and this leads to severe competition. What is left then? How can a company gain competitive advantage? The only thing that can make a difference is not the quality of the product but the quality of the information they posses about the market, the client, the product, the technological process, management etc. It’s about the information management. It’s about competitive intelligence.competitive intelligence, information, intelligence, strategy

Convolution powers in the operator-valued framework

We consider the framework of an operator-valued noncommutative probability space over a unital C*-algebra B. We show how for a B-valued distribution \mu one can define convolution powers with respect to free additive convolution and with respect to Boolean convolution, where the exponent considered in the power is a suitably chosen linear map \eta from B to B, instead of being a non-negative real number. More precisely, the Boolean convolution power is defined whenever \eta is completely positive, while the free additive convolution power is defined whenever \eta - 1 is completely positive (where 1 stands for the identity map on B). In connection to these convolution powers we define an evolution semigroup related to the Boolean Bercovici-Pata bijection. We prove several properties of this semigroup, including its connection to the B-valued free Brownian motion. We also obtain two results on the operator-valued analytic function theory related to the free additive convolution powers with exponent \eta. One of the results concerns analytic subordination for B-valued Cauchy-Stieltjes transforms. The other gives a B-valued version of the inviscid Burgers equation, which is satisfied by the Cauchy-Stieltjes transform of a B-valued free Brownian motion.Comment: 33 pages, no figure

A comparison of freezing-damage during isochoric and isobaric freezing of the potato.

BACKGROUND:Freezing is commonly used for food preservation. It is usually done under constant atmospheric pressure (isobaric). While extending the life of the produce, isobaric freezing has detrimental effects. It causes loss of food weight and changes in food quality. Using thermodynamic analysis, we have developed a theoretical model of the process of freezing in a constant volume system (isochoric). The mathematical model suggests that the detrimental effects associated with isobaric freezing may be reduced in an isochoric freezing system. To explore this hypothesis, we performed a preliminary study on the isochoric freezing of a produce with which our group has experience, the potato. METHOD:Experiments were performed in an isochoric freezing device we designed. The device is robust and has no moving parts. For comparison, we used a geometrically identical isobaric freezing device. Following freezing and thawing, the samples were weighed, examined with colorimetry, and examined with microscopy. RESULTS:It was found that potatoes frozen to -5 °C in an isochoric system experienced no weight loss and limited enzymatic browning. In contrast the -5 °C isobaric frozen potato experienced substantial weight loss and substantial enzymatic browning. Microscopic analysis shows that the structural integrity of the potato is maintained after freezing in the isochoric system and impaired after freezing in the isobaric system. DISCUSSION:Tissue damage during isobaric freezing is caused by the increase in extracellular osmolality and the mechanical damage by ice crystals. Our thermodynamic analysis predicts that during isochoric freezing the intracellular osmolality remains comparable to the extracellular osmolality and that isochoric systems can be designed to eliminate the mechanical damage by ice. The results of this preliminary study seem to confirm the theoretical predictions. CONCLUSION:This is a preliminary exploratory study on isochoric freezing of food. We have shown that the quality of a food product preserved by isochoric freezing is better than the quality of food preserved to the same temperature in isobaric conditions. Obviously, more extensive research remains to be done to extend this study to lower freezing temperatures and other food items

The treatment of superficial bladder tumors with BCG

Urology Clinic of Targu Mures County Hospital, Romania, The 6th International Medical Congress for Students and Young Doctors, May 12-14, 2016Introduction: Bladder cancer is the 5th most common type of neoplasm regarding to incidence. Smoking is the primary risk factor in developing bladder cancer. Previous studies have shown that approximately 70% of the bladder tumors are nonmuscle invasive bladder cancer (NMIBC). Mycobacterium bovis bacillus Calmette-Guerin (BCG) is currently the standard conservative treatment of NMIBC. Material and methods: We performed a retrospective study, conducted during 6 years from 2010 to 2016 at the Urology Clinic of Tg-Mures County Hospital with a total of 78 patients diagnosed with NMIBC.We analyzed the following variables: age, gender, histopathological result, the number of BCG infiltration, in the first six weeks one every week, at three and six months, cystoscopy and the rate of relapse, the main criteria of evaluating the results of the treatment. Results: In the study that we conducted we had a number of 15 women (19,2%) and 63 men (80,8%). At the end of the first six weeks 89,7% of the patients completed all six infiltrations, 70,5% at 3 months and only 60,3% at 6 months. The results of cystoscopy were normal at 70,5%, 25, 6% did not have a cystoscopy performed. Patients were called for investigations first at three months, six months in the first year after finishing the therapy and then every year. In 63,8% of the patients who had the 6 month therapy, no relapse tumor was found in favor of 14,9% with relapse tumor