Abstract:
Tourism in Romania in the last decade. Case study: the city of Brasov. The urbanization is a phenomenon that took proportions lately, due to the economical development, of transports, of the socio-cultural interests, to the increase of the education level, etc. Due to the means of information, communication, and transport and to the concentration of the touristic historical-cultural objectives inthe big cities, these ones have become important points of attraction for the touristic activity. In the last decade, due to the economic restructuring and to the increase of the role of the services sector, tourism has begun to have an important contribution in the economy of the country including the city of Brasov. In Romania, the city of Brasov represents one of the most important touristic centresof the country due to the numerous historical and cultural objectives within it but also the special natural resources. Although tourism has become one of the main factors concerning the economical development, we cannot ignore the negative aspects that result as a consequence of the touristic activity that is why it is necessary that this one should take place in the conditions in which the actual generation to beneficiate and use the current natural and anthropic resources sothat the next generations can take advantage of as well.

Abstract:
Vu, Wood and Wood showed that any finite set S in a characteristic zero integral domain can be mapped to F_p, for infinitely many primes p, while preserving finitely many algebraic incidences of S. In this note we show that the converse essentially holds, namely any small subset of F_p can be mapped to some finite algebraic extension of Q, while preserving bounded algebraic relations. This answers a question of Vu, Wood and Wood. We give several applications, in particular we show that for small subsets of F_p, the Szemer\'edi-Trotter theorem holds with optimal exponent 4/3, and we improve the previously best-known sum-product estimate in F_p. We also give an application to an old question of R\'enyi. The proof of the main result is an application of elimination theory and is similar in spirit with the proof of the quantitative Hilbert Nullstellensatz.

Abstract:
The present paper is concerned with the various algebraic structures supported by the set of Tur\'an densities. We prove that the set of Tur\'an densities of finite families of r-graphs is a non-trivial commutative semigroup, and as a consequence we construct explicit irrational densities for any even r >= 4. The proof relies on a technique recently developed by Pikhurko. We also show that the set of all Tur\'an densities forms a graded ring, and from this we obtain a short proof of a theorem of Peng on jumps of hypergraphs. Finally, we prove that the set of Tur\'an densities of families of r-graphs has positive Lebesgue measure if and only if it contains an open interval. This is a simple consequence of Steinhaus's theorem.

Abstract:
More than a century after its proposal, the Towers of Hanoi puzzle with 4 pegs was solved by Thierry Bousch in a breakthrough paper in 2014. The general problem with p pegs is still open, with the best lower bound on the minimum number of moves due to Chen and Shen. We use some of Bousch's new ideas to obtain an asymptotic improvement on this bound for all p >= 5.

Abstract:
DFNB1 locus has been linked to a nonsyndromic “invisible disability” called congenital sensorineural hearing loss and deafness. Mutations of GJB2 and GJB6 genes are associated with deafness at the DFNB1 locus. The diagnosis of DFNB1 is made with molecular genetic testing. DNA-based testing can be used both prenatally and postnatally. Purpose: to get evidence for implementation of newborn hearing screening programs at national level; to use the molecular testing of children at risk for confirmation of diagnosis and early intervention. OAEs and ABR were performed for 4303 newborns. Audiologic evaluation of 38 children suspected of having hearing loss was performed too. Physical examinations and family history were used to get information about congenital deafness. DNA from blood samples was isolated, and two PCR multiplex assays were developed to detect DFNB1 mutations. Only 23 newborns were screened positive. Newborns were referred to audiologic evaluation, genetic counseling and testing for the etiologic diagnosis. Physical examination revealed no other abnormal findings. GJB2 mutations were detected in 36.03% of patients, and all of them have 35delG mutation. None of them was found to have GJB6 mutations. Our results suggested that molecular testing was an accurate method of early determining cause of congenital hearing loss and helped us to exclude GJB6 gene from the routine hearing screening protocol.

Abstract:
Let r >= s >= 0 be integers and G be an r-graph. The higher inclusion matrix M_s^r(G) is a {0,1}-matrix with rows indexed by the edges of G and columns indexed by the subsets of V(G) of size s: the entry corresponding to an edge e and a subset S is 1 if S is contained in e and 0 otherwise. Following a question of Frankl and Tokushige and a result of Keevash, we define the rank-extremal function rex(n,t,r,s) as the maximum number of edges of an r-graph G having rank M_s^r(G) <=\binom{n}{s} - t. For t at most linear in n we determine this function as well as the extremal r-graphs. The special case t=1 answers a question of Keevash.

Abstract:
Squamous cell cancer (ESCC) and adenocarcinoma (EADC) are the two main subtypes of oesophageal cancer. Genetic alterations associated with the development of oesophageal cancer are often observed. The aim of this study was to identify p53 gene polymorphisms in several patients with oesophageal squamous cell carcinoma. Genomic DNA was isolated from normal-, tumor- and blood-samples from patients with ESCC. PCR amplification of two p53 gene fragments was performed using two sets of primers DNA samples were sequenced and then analyzed with BLAST program Exons 5, 7 and 8 did not present mutations for the studied patients, but exon 6 featured one modification in two different patients. The mutations of p53 gene can determine the modification of its proteine function and the loss of its antioncogene role, which reflects the abnormal proliferation of the cells implicated in this type of cancer.

We present an approach how to obtain solutions of arbitrary linear operator equation for unknown functions. The particular solution can be represented by the infinite operator series (Cyclic Operator Decomposition), which acts the generating function. The method allows us to choose the cyclic operators and corresponding generating function selectively, depending on initial problem for analytical or numerical study. Our approach includes, as a particular case, the perturbation theory, but generally does not require inside any small parameters and unperturbed solutions. We demonstrate the applicability of the method to the analysis of several differential equations in mathematical physics, namely, classical oscillator, Schrodinger equation, and wave equation in dispersive medium.

Abstract:
Purpose: We assess the significance of dyscirculatory angiopathy of Alzheimer’s type (DAAT) in identify- ing the predisposition to the development and diagnosis of Alzheimer’s disease (AD) different stages. Meth- ods: 108 patients took part in the research:1) 49 aged 34-79 suffering from AD or running an increased risk of its development (those not diagnosed with AD but having growing memory disorders without any mani- festations of dementia or specific cognitive impairments, and having 2 or more immediate relatives with AD) - Test Group; 2) 59 aged 28-78 suffering from different types of brain lesions accompanied by dementia but not suffering from AD or corresponding to their age norm - Control Group. All the patients underwent MRI, CT with subsequent calculation of the temporal lobes atrophy degree, brain scintigraphy (SG), rheoencepha- lography (REG), and MUGA. Results: Characteristic features of patients with an increased risk of AD as well as at its various stages are: 1) Temporal lobes and hippocampus atrophy ranging from 4% among those with an increased risk of AD to 62% among those at its advanced stages; 2) DAAT manifestations: reduction of the capillary bed in the temporal and frontoparietal regions with the development of multiple arterioven- ous shunts of the same localization and correspondent early venous discharge accompanied by venous stasis on the border of the frontal and parietal region; 3) DAAT phenomena equally develop both among those with an increased risk of developing AD and those at various AD stages. Similar changes are not observed among Control Group patients with other brain lesions, regardless of the severity of dementia, as well as among practically healthy people of the corresponding age group. Conclusion: Timely identification of the above- mentioned changes can reveal a predisposition to AD development long before its initial manifestations, and it allows differentiating AD from other diseases attended by dementia. In both cases, timely diagnosis allows beginning timely treatment and thus achieving more stable results.