Univalence and starlikeness of certain transforms defined by convolution of analytic functions

AbstractLet U(λ) denote the class of all analytic functions f in the unit disk Δ of the form f(z)=z+a2z2+⋯ satisfying the condition|f′(z)(zf(z))2−1|⩽λ,z∈Δ. In this paper we find conditions on λ and on c∈C with Rec⩾0≠c such that for each f∈U(λ) satisfying (z/f(z))∗F(1,c;c+1;z)≠0 for all z∈Δ the transformG(z)=Gfc(z)=z(z/f(z))∗F(1,c;c+1;z),z∈Δ, is univalent or starlike. Here F(a,b;c;z) denotes the Gauss hypergeometric function and ∗ denotes the convolution (or Hadamard product) of analytic functions on Δ

On harmonic combination of univalent functions

Let ${\mathcal S}$ be the class of all functions $f$ that are analytic and univalent in the unit disk \ID with the normalization $f(0)=f'(0)-1=0$. Let $\mathcal{U} (\lambda)$ denote the set of all $f\in {\mathcal S}$ satisfying the condition |f'(z)(\frac{z}{f(z)})^{2}-1| <\lambda ~for $z\in \ID$, for some $\lambda \in (0,1]$. In this paper, among other things, we study a "harmonic mean" of two univalent analytic functions. More precisely, we discuss the properties of the class of functions $F$ of the form $$\frac{z}{F(z)}=1/2(\frac{z}{f(z)}+\frac{z}{g(z)}),$$ where $f,g\in \mathcal{S}$ or $f,g\in \mathcal{U}(1)$. In particular, we determine the radius of univalency of $F$, and propose two conjectures concerning the univalency of $F$.Comment: 10 pages. the article is with a journa

Identification and molecular characterization of Chryseobacterium vrystaatense ST1 isolated from oligomineral water of southeast Serbia

The isolation and molecular characterization of bacterial strains isolated from water sources in the Vlasina Mountain in southeast Serbia, confirmed the presence of a new species Chryseobacterium vrystaatense ST1. This Gram- negative species showed an extremely low level of biochemical reactivity in biochemical tests. The gene for 16S rRNA was amplified by PCR using universal primers and sequenced. Comparison of 16S rRNA gene sequence and phenotypic features indicated that the isolate ST belonged to Chryseobacterium vrystaatense. A BLAST search of sequenced 1088 nucleotides of the 16S rRNA gene with all sequences deposited in the NCBI collection showed the highest similarity (98%) with the strain Chryseobacterium vrystaatense sp. nov., designated as strain R-23533. The very high homology of these two strains allowed classification of our strain at the species level, but some differences indicate, and indirectly confirm, that the isolate ST is an authentic representative. On the basis of these results, we could conclude that Chryseobacterium vrystaatense ST was for first time isolated in Serbia, which is particularly important when one bears in mind that there are only three sequences of this species deposited in the NCBI collection

On the properties of the concave antiprisms of second sort

Rad se bavi ispitivanjem geometrijskih, statičkih i dinamičkih osobina jedne poliedarske strukture nastale nabiranjem dvorednog segmenta mreže jednakostraničnih trouglova. Osnove ovih konkavnih poliedara su pravilni, identični poligoni u paralelnim ravnima, povezani nizom naizmeničnih trouglova, kao i u slučaju konveksnih antiprizmi. Postoje dve varijante savijanja ovakve mreže, pa samim tim i dva tipa konkavnih antiprizmi druge vrste (KA II) za svaku posmatranu osnovu od n=5, n=∞. U radu su razmotreni načini dobijanja tačnog položaja temena i drugih linearnih parametara ovih poliedara, uz primenu algoritma za njihovo matematičko izračunavanje. Strukturalna analiza jednog predstavnika ovih poliedara data je korišćenjem aplikacija programa SolidWorks, kako bi se ispitala mogućnost primene ovih oblika u inženjerstvu.The paper examines geometrical, static and dynamic properties of the polyhedral structures obtained by folding and creasing the two-rowed segment of equilateral triangular net. Bases of these concave polyhedra are regular, identical polygons in parallel planes, connected by the alternating series of triangles, as in the case of convex antiprisms. There are two ways of folding such a net, and therefore the two types of concave antiprisms of second sort. The paper discusses the methods of obtaining the accurate position of the vertices and other linear parameters of these polyhedra, with the use of mathematical algorithm. Structural analysis of a representative of these polyhedra is presented using the SolidWorks program applications

Identification and molecular characterization of Chryseobacterium vrystaatense ST1 isolated from oligomineral water of southeast Serbia

The isolation and molecular characterization of bacterial strains isolated from water sources in the Vlasina Mountain in southeast Serbia, confirmed the presence of a new species Chryseobacterium vrystaatense ST1. This Gram- negative species showed an extremely low level of biochemical reactivity in biochemical tests. The gene for 16S rRNA was amplified by PCR using universal primers and sequenced. Comparison of 16S rRNA gene sequence and phenotypic features indicated that the isolate ST belonged to Chryseobacterium vrystaatense. A BLAST search of sequenced 1088 nucleotides of the 16S rRNA gene with all sequences deposited in the NCBI collection showed the highest similarity (98%) with the strain Chryseobacterium vrystaatense sp. nov., designated as strain R-23533. The very high homology of these two strains allowed classification of our strain at the species level, but some differences indicate, and indirectly confirm, that the isolate ST is an authentic representative. On the basis of these results, we could conclude that Chryseobacterium vrystaatense ST was for first time isolated in Serbia, which is particularly important when one bears in mind that there are only three sequences of this species deposited in the NCBI collection

Molecular and biochemical characterization of pseudomonas putida isolated from bottled uncarbonated mineral drinking water

Pseudomonas putida belongs to a group of opportunistic pathogens that can cause disease in people with weakened or damaged immune systems. Some strains have medical significance, and for most ingestion is not the primary route of infection. If water used by predisposed subjects is contaminated by P. putida, they may become ill. The aim of this work was the biochemical and molecular characterization of strain ST3 of P. putida isolated from non-carbonated bottled drinking water from Jakov Do 4 on Mt. Vlasina. Characterization of P. putida was performed to assess the risk to human health of the indigenous strains present in the water. Biochemical characterization of strains was performed using the manual identification system ID 32 GN (BioMerieux). Identification was obtained using the database identification software ATB System (Bio-Merieux). Molecular characterization was performed by PCR amplification and 16S rDNA "thermal cycling sequencing". Biochemical identification of the strain ST3 was accurate (Id = 99.8%). Comparing the sequences obtained for strain ST3 with NCBI gene bank sequences for 16S rRNA, the highest similarity of our strain (96% identity) with a strain of P. putida, designated as biotype A (gi vertical bar 18076625 vertical bar emb vertical bar AJ308311.1 vertical bar.PPU308311) isolated in New Zealand, was obtained. While comparison with the NCBI collection of all deposited sequences showed that the 16S rRNA gene sequence of strain ST3 has very high homology, it is not identical, indicating indirectly that strain ST-3 is an indigenous strain

Injectivity of sections of convex harmonic mappings and convolution theorems

In the article the authors consider the class ${\mathcal H}_0$ of sense-preserving harmonic functions $f=h+\overline{g}$ defined in the unit disk $|z|<1$ and normalized so that $h(0)=0=h'(0)-1$ and $g(0)=0=g'(0)$, where $h$ and $g$ are analytic in the unit disk. In the first part of the article we present two classes $\mathcal{P}_H^0(\alpha)$ and $\mathcal{G}_H^0(\beta)$ of functions from ${\mathcal H}_0$ and show that if $f\in \mathcal{P}_H^0(\alpha)$ and $F\in\mathcal{G}_H^0(\beta)$, then the harmonic convolution is a univalent and close-to-convex harmonic function in the unit disk provided certain conditions for parameters $\alpha$ and $\beta$ are satisfied. In the second part we study the harmonic sections (partial sums) $$s_{n, n}(f)(z)=s_n(h)(z)+\overline{s_n(g)(z)},$$ where $f=h+\overline{g}\in {\mathcal H}_0$, $s_n(h)$ and $s_n(g)$ denote the $n$-th partial sums of $h$ and $g$, respectively. We prove, among others, that if $f=h+\overline{g}\in{\mathcal H}_0$ is a univalent harmonic convex mapping, then $s_{n, n}(f)$ is univalent and close-to-convex in the disk $|z|< 1/4$ for $n\geq 2$, and $s_{n, n}(f)$ is also convex in the disk $|z|< 1/4$ for $n\geq2$ and $n\neq 3$. Moreover, we show that the section $s_{3,3}(f)$ of $f\in {\mathcal C}_H^0$ is not convex in the disk $|z|<1/4$ but is shown to be convex in a smaller disk.Comment: 16 pages, 3 figures; To appear in Czechoslovak Mathematical Journa

Principles of architectural heritage and their contemporary implementation

Основни циљ рада је препознавање начела градитељског предања и одговор на питање да ли се и како уочени принципи народног градитељства могу применити у савременом процесу пројектовања. Aнализом примера, изабраних на основу успостављених критеријума, из непрегледне ризнице народног градитељског стваралаштва на територији данашње Републике Србије, шире гледано Балканског полуострва, сагледана су и формулисана основна начела градитељског предања. Она показују како је народ градио у складу са поднебљем, особинама тла, климатским условима, биљним покривачем и својим потребама, својом духовном и културном традицијом. У раду су дефинисане оне универзалне карактеристике, принципи и модели који су примењиви и ван примарног контекста у коме су настали. Секундарни циљ истраживања је сагледавање могућности примене препознатих начела градитељског предања у савременој пракси урбанистичко-архитектонског пројектовања групација и појединачних објеката. У завршном делу рада, на конкретном примеру из праксе, дата је анализа могућности савремене примене традиционалних принципа грађења Основни метод примењен у овом истраживању је аналитички, а који у односу на анализиране поједине примере предачког градитељства добија и елементе описног, структуралног, историографског, компаративног и интуитивног. Применом наведених метода дошло се до података, не само из области народног начина грађења, већ и из области духовног стваралаштва, обреда, вере и предања, наслеђених обичаја и неписаних правила за живот и грађење куће и осталих објеката и уређаја око ње. Анализом структуре групација и појединачно објеката, узрочно последичним повезивањем градитељског одговора на животне VI потребе становника, под утицајем културних и духовних наслага и уплива, искристалисана су начела на основу познатих појмова и односа, сада сагледаних на другачији, али комплементарни начин него што то чини етнологија и заштита народног градитељства...The basic aim of this work is how to recognize the principles of architectural tradition and to analyze whether and how these principles of national folk building could be implemented within the modern process of design. The analysis of examples, chosen from the inexhaustible treasury of traditional folkways building creativity on the territory of the present Republic of Serbia (and the Balkan Peninsula in a larger sense), according to established criteria, has led to the understanding and elaboration of the basic principles of architectural tradition. They show how people have built and constructed in conformity with climatic conditions, soil characteristics, flora and according to their needs, their spiritual and cultural tradition. The universal characteristics, principles and models that are applicable even outside the primary context in which they had appeared have been defined in this work. The secondary aim of research has been to observe the possibilities of implementing the recognized principles of architectural tradition today in the modern practice of urban planning and architectural design of group and individual buildings. The final part of the work is devoted to the analysis of actual possibilities of implementation of traditional building practice in the practice of architects today. The basic method applied here is the analytical one. However, in relation to the analyzed individual examples of traditional (ancestral) architecture it has acquired certain descriptive, structural, historiographic, comparative and intuitive elements. The use of these methods resulted in obtaining data not only on the folkways type of building, but of spiritual creativity, rites, religion and tradition, inherited customs and unwritten rules on building houses and other structures around them too. The analysis of structures of groups and individual buildings, by connecting the builders response to existential needs of the population under the influence of cultural and spiritual layers and influences, has led to crystallization of principles based upon known notions and relations, now understood in a different, but complementary way, compared to the explanation given by ethnology and the protection of folkways building practice..

Analysis of isothermal sintering of zinc-titanate doped with MgO

The aim of this work was analysis of isothermal sintering of zinc titanate ceramics doped with MgO obtained by mechanical activation. Mixtures of ZnO, TiO2 and MgO (0, 1.25 and 2.5%) were mechanically activated 15 minutes in a planetary ball mill. The powders obtained were pressed under different pressures and the results were fitted with a phenomenological compacting equation. Isothermal sintering was performed in air for 120 minutes at four different temperatures. Structural characterization of ZnO-TiO2-MgO system after milling was performed at room temperature using XRPD measurements. DTA measurements showed different activation energies for pure and doped ZnO-TiO2 systems. Thus addition of MgO stabilizes the crystal structure of zinc titanate