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The paper presents an electronic self-oscillation acoustic system (SAS) destined to measure of stresses variations in the elastic media. The system consists of piezoelectric detector, amplifier-limiter, pass-band filter, piezoelectric exciter and the frequency meter. The mass rock plays a role of delaying element, in which variations in stresses causing the variations of acoustic wave velocity of propagation, and successive variation in frequency of oscillations generated by system. The laboratory test permitted to estimate variations in frequency caused by variations in stresses of elastic medium. The principles of selection of frequency and other parameters of the electronic system in application to stresses measurement in condition of the mine were presented., Comment: 11 pages, 11 figures

The quasi-binary phase diagram lithium oxide - molybdenum(VI) oxide was investigated by differential scanning calorimetry and X-ray diffraction. The four intermediate phases Li4MoO5, Li2MoO4, Li4Mo5O17, and Li2Mo4O13 show incongruent melting. The system has one eutectic point at 50.5 mol% MoO3 and 49.5 mol% LiO0.5 with a eutectic temperature of 524.6 deg C. At this point the melt is in equilibrium with Li2MoO4 and Li4Mo5O17., Comment: excerpt from a published article, with 3 figures and 1 table

Recently we had derived a new type generalized binomials mixed recurrence for primordial sequence case . Here we report on this new type mixed V and U binomials recurrence in brief., Comment: 11 pages, 0 figures

The binary phase diagram of the YAlO3 (YAP) - NdAlO3 (NAP) system was determined by differential thermal analysis (DTA) and X-ray powder diffraction (XRD) measurements. High purity nanocrystalline powders and small single crystals of Y_{1-x}Nd_{x}AlO_3 (0 \leq x \leq 1) have been produced successfully by modified sol-gel (Pechini) and micro-pulling-down methods, respectively. Both end members show high mutual solubility >25% in the solid phase, with a miscibility gap for intermediate compositions. A solid solution with x \approx 0.2 melts azeotropic ca. 20 degrees below pure YAP. Such crystals can be grown from the melt without segregation. The narrow solid/liquid region near the azeotrope point could be measured with a "cycling" DTA measurement technique., Comment: 12 pages, 8 figures, submitted to J. Alloys. Compd

We deliver here second new $\textit{H(x)}-binomials'$ recurrence formula, were $H(x)-binomials' $ array is appointed by $Ward-Horadam$ sequence of functions which in predominantly considered cases where chosen to be polynomials . Secondly, we supply a review of selected related combinatorial interpretations of generalized binomial coefficients. We then propose also a kind of transfer of interpretation of $p,q-binomial $ coefficients onto $q-binomial$ coefficients interpretations thus bringing us back to $Gy{\"{o}}rgy P\'olya $ and Donald Ervin Knuth relevant investigation decades ago., Comment: 57 pages, 8 figures

We deliver here H(x)binomials recurrence formula appointed by Ward Horadam sequence of functions which in mostly considered since decades cases where chosen to be polynomials ., Comment: 35 pp

The looked for V-binomials recurrence for Lucas companion to $U_n$ sequence $V_n$ is delivered, Comment: 9 pages

It is shown that a C*-algebra generated by any faithful covariant representation of a Hilbert bimodule X is canonically isomorphic to the crossed product associated to X provided that Rieffel's induced representation functor X-ind is topologically free. It is discussed how this result could be applied to universal C*-algebras generated by relations with a circle gauge action. In particular, it leads to generalizations of isomorphism theorems for various crossed products, and is shown to be equivalent to Cuntz-Krieger uniqueness theorem for finite graph C*-algebras (on that occasion an intriguing realization of Cuntz-Krieger algebras as crossed products by Exel's interactions is discovered)., Comment: This paper has been withdrawn by the author. The results of the paper are presented in a more accurate and extended form in the following published papers: Topological freeness for Hilbert bimodules (arXiv:1212.0361), Crossed products for interactions and graph algebras (arXiv:1301.5125), Ideal structure of crossed products by endomorphisms via reversible extensions of C*-dynamical systems (arXiv:1404.4928)

A construction of reversible extensions of dynamical systems which applies to arbitrary mappings (not necessarily with open range) is presented. It is based on calculating the maximal ideal space of C*-algebras that extends endomorphisms to partial automorphisms via partial isometric representations, and involves a newfound set of "parameters" (the role of parameters play chosen sets or ideals). Additionally, it is characterised as a universal object. As model examples, we give a thorough description of reversible extensions of logistic maps, and a classification of systems associated with compression of unitaries generating homeomorphisms of the circle., Comment: 39 pages, 18 figures

X-ray Photon Correlation Spectroscopy (XPCS) has emerged as a unique technique allowing the measurement of dynamics in materials on mesoscopic lengthscales. In particular, applications in soft matter physics cover a broad range of topics which include, but are not limited to, nanostructured materials such as colloidal suspensions or polymers, dynamics at liquid surfaces, membranes and interfaces, and the glass or gel transition. One of the most common problems associated with the use of bright X-ray beams with soft materials is beam induced radiation damage, and this is likely to become an even more limiting factor at future synchrotron and free electron laser sources. Flowing the sample during data acquisition is one of the simplest method allowing to limit the radiation damage. In addition to distributing the dose over many different scatterers, the method also enables new functionalities such as time-resolved studies in mixing cells. Here, we further develop an experimental technique that was recently proposed combining XPCS and continuously flowing samples. More specifically, we use a model system to show how the macroscopic advective response to flow and the microscopic dissipative dynamics (diffusion) can be quantified from the X-ray data. The method has many potential applications, e.g. dynamics of glasses and gels under continuous shear/flow, protein aggregations processes, the interplay between dynamics and rheology in complex fluids., Comment: 11 pages, 5 figures

In addition to the three standard operations on posets which are dual of poset or ordinal and cardinal sums of partial ordered sets one adds the natural join of posets. This is especially natural natural join operation for graded posets including very special and important the so called cobweb posets. The main aims of this article are the presentation of the authors update applications of natural join of posets in the domain of graded posets and summary of the general properties of natural join of posets with posing some questions arising on the way. Thus in this note apart from revealing some general properties of natural join of posets we also deliver the authors combinatorial interpretations of cobweb posets including discrete hyperboxes coding of the so called cobweb posets .Various explicit formulas for the zeta functions and zeta matrices as well as the inverse of zeta matrix for any graded posets are supplied. Whitney numbers formulas and those for characteristic polynomials are given too., Comment: 34 pages 16 figures The Internet Gian-Carlo Rota Polish Seminar article http://ii.uwb.edu.pl/akk/sem/sem\_rota.htm

One introduces here the natural join $P \os Q$ of graded posets $< P,\leq_P >$ and $< Q,\leq_Q >$ with correspondingly maximal and minimal sets being identical as expressed by ordinal sum $P\oplus Q$ apart from other definition and due to that one arrives at a simple proof of the $M{\"{o}}bius $ function formula for cobweb posets. We also quote the other authors explicit formulas for the zeta matrix and its inverse for any graded posets with the finite set of minimal elements from earlier works of the author. These formulas are based on the formulas for cobweb posets and their $Hasse$ diagrams or graphs named $KoDAGs$ which are interpreted as chains of binary complete or universal relations joined by the natural join operation. Natural join of two independent sets is therefore the ordinal sum of this trivially ordered posets represented also by directed biclique named dibiclique and correspondingly by their $Hasse $ diagrams or graphs named $KoDAGs$. Such cobweb posets and equivalently their Hasse diagrams or graphs named $KoDAGs$ are also encoded by discrete hyper-boxes and the natural join operation of such discrete hyper boxes is just cartesian product of them accompanied with projection out of common faces. All graded posets with no mute vertices in their $Hasse$ diagrams which means that no vertex has indegree or outdegree equal zero are natural join of chain of relations and may be at the same time interpreted an $n-ary$ relation, $n \in N \cup \{\infty \}$., Comment: 51 pages, 11 figures, The Internet Gian-Carlo Rota Polish Seminar article http://ii.uwb.edu.pl/akk/sem/sem\_rota.htm

We introduce and analyse the structure of C*-algebras arising from ideals in right tensor C*-precategories, which naturally generalize both relative Cuntz-Pimsner and Doplicher-Roberts algebras. We establish an explicit intrinsic construction of the considered algebras and a number of key results such as structure theorem, gauge-invariant uniqueness theorem or description of the gauge-invariant ideal structure. In particular, these statements give a new insight into the corresponding results for relative Cuntz-Pimsner algebras and are applied to Doplicher-Roberts associated to C*-correspondences.

We derive the explicit formula for the inverse of zeta matrix for any graded posets with the finite set of minimal elements . The combinatorial interpretation of this result is given. For that to do special number theoretic code triangles for graded posets are proposed and apart from the present author combinatorial interpretation of $F-nomial$ coefficients another one is proposed referring to the number of all maximal chains in the corresponding poset intervals., Comment: 48 pages, 7 figures, affiliated to The Internet Gian-Carlo Polish Seminar: http://ii.uwb.edu.pl/akk/sem/sem_rota.htm

One outlines here in brief how the work of $Gian Carlo Rota$ had influenced my group research and life, starting from the end of the last century up to present time state of $The Internet Gian Carlo Rota Polish Seminar$. This note has been written for the $Rota Memorial Conference$ to be held on 16-18 Feb 2009, Milan, Italy., Comment: 5pages, 1 figure, affiliated to The Internet Gian-Carlo Polish Seminar: http://ii.uwb.edu.pl/akk/sem/sem_rota.htm

The way to arrive at formula of zeta matrix for any graded posets with the finite set of minimal elements is delivered following the first reference. This is being achieved via adjacency and zeta matrix description of bipartite digraphs chains, the representatives of graded posets. The bipartite digraphs elements of such chains amalgamate to form corresponding cover relation graded poset digraphs with corresponding adjacency matrices being amalgamated throughout natural join as special adequate database operation. The colligation of reachability and connectivity with the presented description is made explicit. The special posets encoded via kodags directed acyclic graphs as cobeb posets cover relations digraphs are recognized as an example of differential posets subfamily. As on this night one reminisce anniversary of death of distinguished johann bernoulli the first this sylvester night article is to commemorate this date., Comment: 15 pages, affiliated to The Internet Gian-Carlo Rota Polish Seminar http://ii.uwb.edu.pl/akk/sem/sem_rota.htm

A calculus of sequences started by professor morgan ward constitutes the general scheme for extensions of classical operator calculus of the distinguished gian carlo rota considered by many afterwards and after ward morgan. Because of the historically now established notation we call the wardian calculus of sequences in its afterwards elaborated form a psi calculus. The psi calculus in parts appears to be almost automatic, natural extension of classical operator calculus or equivalently of umbral calculus . This is a review article based on the turn of the centuries author relevant contributions., Comment: 24 pages, affiliated to The Internet Gian-Carlo Polish Seminar http://ii.uwb.edu.pl/akk/sem/sem_rota.htm

Natural join of $di-bigraphs$ that is directed biparted graphs and their corresponding adjacency matrices is defined and then applied to investigate the so called cobweb posets and their $Hasse$ digraphs called $KoDAGs$. $KoDAGs$ are special orderable directed acyclic graphs which are cover relation digraphs of cobweb posets introduced by the author few years ago. $KoDAGs$ appear to be distinguished family of $Ferrers$ digraphs which are natural join of a corresponding ordering chain of one direction directed cliques called $di-bicliques$. These digraphs serve to represent faithfully corresponding relations of arbitrary arity so that all relations of arbitrary arity are their subrelations. Being this $chain -way$ complete if compared with kompletne $Kuratowski$ bipartite graphs their $DAG$ denotation is accompanied with the letter $K$ in front of descriptive abbreviation $oDAG$. The way to join bipartite digraphs of binary into $multi-ary$ relations is the natural join operation either on relations or their digraph representatives. This natural join operation is denoted here by $\os$ symbol deliberately referring to the direct sum $\oplus$ of adjacency matrices as it becomes the case for disjoint $di-bigraphs$., Comment: 19 pages, 7 figures,affiliated to The Internet Gian-Carlo Polish Seminar: http://ii.uwb.edu.pl/akk/sem/sem_rota.htm

One considers here orderable acyclic digraphs named KoDAGs which represent the outmost general chains of dibicliques denoting thus the outmost general chains of binary relations. Because of this fact KoDAGs start to become an outstanding concept of nowadays investigation. We propose here examples of codings of KoDAGs looked upon as infinite hyper-boxes as well as chains of rectangular hyper-boxes in N^\infty. Neither of KoDAGs codings considered here is a poset isomorphism with Pi = . Nevertheless every example of coding supplies a new view on possible investigation of KoDAGs properties. The codes proposed here down are by now recognized as most relevant codes for practical purposes including visualization. More than that. Employing quite arbitrary sequences F=\{n_F\}_{n\geq 0} infinitely many new representations of natural numbers called base of F number system representations are introduced. These constitute mixed radix-type numeral systems. F base nonstandard positional numeral systems in which the numerical base varies from position to position have picturesque interpretation due to KoDAGs graphs and their correspondent posets which in turn are endowed on their own with combinatorial interpretation of uniquely assigned to KoDAGs F-nomial coefficients. The base of F number systems are used for KoDAGs coding and are interpreted as chain coordinatization in KoDAGs pictures as well as systems of infinite number of boxes sequences of F-varying containers capacity of subsequent boxes. Needless to say how crucial is this base of F number system for KoDAGs hence consequently for arbitrary chains of binary relations. New F based numeral systems are umbral base of F number systems in a sense to be explained in what follows., Comment: 26 pages, 15 figures, Presented at Gian-Carlo Polish Seminar: http://ii.uwb.edu.pl/akk/sem/sem_rota.htm

Extensions of the $Stirling$ numbers of the second kind and $Dobinski$ -like formulas are proposed in a series of exercises for graduates. Some of these new formulas recently discovered by me are to be found in the source paper $ [1]$. These extensions naturally encompass the well known $q$- extensions. The indicatory references are to point at a part of the vast domain of the foundations of computer science in arxiv affiliation., Comment: 9 pages, presented at the Gian-Carlo Rota Polish Seminar, http://ii.uwb.edu.pl/akk/sem/sem_rota.htm

A research problem for undergraduates and graduates is being posed as a cap for the prior antecedent regular discrete mathematics exercises. [Here cap is not necessarily CAP=Competitive Access Provider, though nevertheless ...] The object of the cap problem of final interest i.e. array of fibonomial coefficients and the issue of its combinatorial meaning is to be found in A.K.Kwa\'sniewski's source papers. The cap problem number seven - still opened for students has been placed on Mathemagics page of the first author [http://ii.uwb.edu.pl/akk/dydaktyka/dyskr/dyskretna.htm]. The indicatory references are to point at a part of the vast domain of the foundations of computer science in ArXiv affiliation noted as CO.cs.DM. The presentation has been verified in a tutor system of communication with a couple of intelligent students. The result is top secret.Temporarily. [Contact: Wikipedia; Theory of cognitive development]., Comment: 4 pages, presented at the Gian-Carlo Rota Polish Seminar, http://ii.uwb.edu.pl/akk/sem/sem_rota.htm, submitted to FECS'08: The 2008 International Conference on Frontiers in Education: WORLDCOMP'08

In this first part of a larger review undertaking the results of the first author and a part of the second author doctor dissertation are presented. Next we plan to give a survey of a nowadays situation in the area of investigation. Here we report on what follows. Calculation of the partition function for any vector potts model is at first reduced to the calculation of traces of products of the generalized clifford algebra generators. The formula for such traces is derived. This enables one, in principle, to use an explicit calculation algorithm for partition functions also in other models for which the transfer matrix is an element from generalized clifford algebra. The method - simple for $Z_2$ case - becomes complicated for $Z_n$, $n>2$, however everything is controlled, in principle, due to knowledge of the corresponding algebra properties and those of generalized cosh function. The discussion of the content of the in statu nascendi second part is to be found at the end of this presentation. This constitutes the last section., Comment: 23 pages

Before we dive into the accessibility stream of nowadays indicatory applications of octonions to computer and other sciences and to quantum physics let us focus for a while on the crucially relevant events for todays revival on interest to nonassociativity. Our reflections keep wandering back to the $Brahmagupta$ $Fibonacc$ two square identity and then via the $Euler$ four square identity up to the $Degen$ $Ggraves$ $Cayley$ eight square identity. These glimpses of history incline and invite us to retell the story on how about one month after quaternions have been carved on the $Broughamian$ bridge octonions were discovered by $John$ $Thomas$ $Ggraves$, jurist and mathematician, a friend of $William$ $Rowan$ $Hamilton$. As for today we just mention en passant quaternionic and octonionic quantum mechanics, generalization of $Cauchy$ $Riemann$ equations for octonions and triality principle and $G_2$ group in spinor language in a descriptive way in order not to daunt non specialists. Relation to finite geometries is recalled and the links to the 7stones of seven sphere, seven imaginary octonions units in out of the $Plato$ cave reality applications are appointed . This way we are welcomed back to primary ideas of $Heisenberg$, $Wheeler$ and other distinguished fathers of quantum mechanics and quantum gravity foundations., Comment: 26 pages, 7 figures

Since the discovery of octonions in 1843 we seem to be still lacking a satisfactory if any theory of octave valued functions satisfactory according to standard requirements or expectation from the side of a theory like a one might look for. Here is a proposal coming back to my twentieth century presentation of a perhaps nonstandard idea hoping to be coping with nonassociativity by an invention., Comment: 14 pages, 1 figure

One delivers here the extended Bernoulli and Taylor formula of a new sort with the rest term of the Cauchy type recently derived by the author in the case of the so called $\psi$-difference calculus which constitutes the representative for the purpose case of extended umbral calculus. The central importance of such a type formulas is beyond any doubt. Recent publications do confirm this historically established experience. Its links via umbrality to combinatorics are known at least since Rota and Mullin source papers then up to recently extended by many authors to be indicated in the sequel., Comment: 11 pages

We introduce a natural partial order in structurally natural finite subsets of the cobweb prefabs sets recently constructed by the present author. Whitney numbers of the second kind of the corresponding subposet which constitute Stirling like numbers triangular array are then calculated and the explicit formula for them is provided. Next, in the second construction we endow the set sums of prefabiants with such an another partial order that their Bell like numbers include Fibonacci triad sequences introduced recently by the present author in order to extend famous relation between binomial Newton coefficients and Fibonacci numbers onto the infinity of their relatives among whom there are also the Fibonacci triad sequences and binomial like coefficients (incidence coefficients included). The first partial order is F sequence independent while the second partial order is F sequence dependent where F is the so called admissible sequence determining cobweb poset by construction. An F determined cobweb posets Hasse diagram becomes Fibonacci tree sheathed with specific cobweb if the sequence F is chosen to be just the Fibonacci sequence. From the stand-point of linear algebra of formal series these are generating functions which stay for the so called extended coherent states of quantum physics. This information is delivered in the last section., Comment: 14 pages

The notion of the Fibonacci cobweb poset from [1] has been naturally extended to any admissible sequence $F$ in [2] where it was also recognized that the celebrated prefab notion of Bender and Goldman [3] - (see also [4,5]) - admits such an extension so as to encompass the new type combinatorial objects from [2] as leading examples. Recently the present author had introduced also [6] two natural partial orders in there: one $\leq$ in grading-natural subsets of cobweb`s prefabs sets [2] and in the second proposal one endows the set sums of the so called "prefabiants" with such another partial order that one arrives at Bell-like numbers including Fibonacci triad sequences introduced by the present author in [7]. Here we quote the basic observations concerning the new type Stirling like numbers as they appear in [6]. For more on notation, Stirling like numbers of the first kind and for proofs - see [6]., Comment: 3 pages

Up to our knowledge -since about 126 years we were lacking of classical type combinatorial interpretation of Fibonomial coefficients as it was Lukas \cite{1} - to our knowledge -who was the first who had defined Finonomial coefficients and derived a recurrence for them (see Historical Note in \cite{2,3}). Here we inform that a join combinatorial interpretation was found \cite{4} for all binomial-type coefficient - Fibonomial coefficients included., Comment: 2 pages

Cobweb posets uniquely represented by directed acyclic graphs are such a generalization of the Fibonacci tree that allows joint combinatorial interpretation for all of them under admissibility condition. This interpretation was derived in the source papers ([6,7] and references therein to the first author).[7,6,8] include natural enquires to be reported on here. The purpose of this presentation is to report on the progress in solving computational problems which are quite easily formulated for the new class of directed acyclic graphs interpreted as Hasse diagrams. The problems posed there and not yet all solved completely are of crucial importance for the vast class of new partially ordered sets with joint combinatorial interpretation. These so called cobweb posets - are relatives of Fibonacci tree and are labeled by specific number sequences - natural numbers sequence and Fibonacci sequence included. The cobweb posets might be identified with a chain of di-bicliques i.e. by definition - a chain of complete bipartite one direction digraphs [6]. Any chain of relations is therefore obtainable from the cobweb poset chain of complete relations via deleting arcs in di-bicliques of the complete relations chain. In particular we response to one of those problems [1]., Comment: 27 pages, 15 figures

The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of graphs i.e. a given graph compositions. The problems result from and are served in the entourage of series of exercises with hints based predominantly on the second reference and other related recent papers., Comment: 12 pages, 4 figures

The article discusses the interrelation between relative Cuntz-Pimsner algebras and partial isometric crossed products, and presents a procedure that reduces any given Hilbert bimodule to the "smallest" Hilbert bimodule yielding the same relative Cuntz-Pimsner algebra as the initial one. In the context of crossed products this reduction procedure corresponds to reduction of C*-dynamical systems., Comment: 13 pages, 1 table

Starting from an arbitrary endomorphism \delta of a unital C*-algebra A we construct a crossed product. It is shown that the natural construction depends not only on the C*-dynamical system (A,\delta) but also on the choice of an ideal J orthogonal to Ker \delta., Comment: 17 pages

Starting from an arbitrary endomorphism $\alpha$ of a unital C*-algebra $A$ we construct a bigger C*-algebra $B$ and extend $\alpha$ onto $B$ in such a way that the extended endomorphism $\alpha$ has a unital kernel and a hereditary range, i.e. there exists a unique non-degenerate transfer operator for $(B,\alpha)$, called the complete transfer operator. The pair $(B,\alpha)$ is universal with respect to a suitable notion of a covariant representation and depends on a choice of an ideal in $A$. The construction enables a natural definition of the crossed product for arbitrary $\alpha$., Comment: Compressed and submitted version, 9 pages

The theme of the paper is the question of existence and basic structure of transfer operators for endomorphisms of a unital C*-algebra. We establish a complete description of non-degenerate transfer operators, characterize complete transfer operators and clarify their role in crossed product constructions. Also, we give necessary and sufficient conditions for existence of transfer operators for commutative systems, and discuss their form for endomorphisms of B(H) which is relevant to Kadison-Singer problem., Comment: 12 pages, to appear in Rocky Mountain J. Math

The paper presents a construction of the crossed product of a C*-algebra by a commutative semigroup of bounded positive linear maps generated by partial isometries. In particular, it generalizes Antonevich, Bakhtin, Lebedev's crossed product by an endomorphism, and is related to Exel's interactions. One of the main goals is the Isomorphism Theorem established in the case of actions by endomorphisms., Comment: 20 pages

The taylor formula pertains historically also to johann or ivan bernoulli. Bernoulli series uiversalisima appeared in acta eruditorum in leipzig when brook taylor was nine years old. As on today one affirms two hundred fifty eight anniversary of death of johann bernoulli this article is proposed also pro memoriam. Very recent extensions of this celebrated formula are indicated in the framework of extended umbral calculus., Comment: 10 pages

The main purpose of this article is to pose three problems which are easy to be formulated in an elementary way. These problems which are specifically important also for the new class of partially ordered sets seem to be not yet solved., Comment: 16 pages, 9 figures, affiliated to The Internet Gian Carlo Rota Polish Seminar: 16 pages, 9 figures, affiliated to The Internet Gian Carlo Rota Polish Seminar http://ii.uwb.edu.pl/akk/sem/sem_rota.htm

We introduce a natural partial order in structurally natural finite subsets the cobweb prefabs sets recently constructed by the present author. Whitney numbers of the second kind of the corresponding subposet which constitute Stirling-like numbers` triangular array are then calculated and the explicit formula for them is provided. Next - in the second construction - we endow the set sums of prefabiants with such an another partial order that their their bell like numbers include fibonacci triad sequences introduced recently by the present author in order to extend famous relation between binomial newton coefficients and fibonacci numbers onto the infinity of their relatives among which there are also the fibonacci triad sequences and binomial-like coefficients (incidence coefficients included)., Comment: 8 pages, 5 figures