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Cellular glass from powders of recycled residual glass, borax as a fluxing agent, and elm leaves as a bio-foaming agent thermally treated at over 825ºC by unconventional microwave heating (according to the own technique) was experimentally manufactured. The wetted mixture was pressed into a mold and then freely inserted into the inner space of a ceramic tube of high microwave susceptible materials placed inside the microwave oven. Ground elm leaves (51 wt. %) were used for the first time as a bio-foaming agent replacing the much more expensive usual foaming agents. The results showed that the cellular glass in the optimal variant is suitable for its application as a heat-insulating building material, having the apparent density of 0.35 g/cm3, thermal conductivity of 0.074 W/m·K, and porosity of 83.3%. Due to the choice of using borax (6 wt. %), the compressive strength of the foam was improved, the 2.5 MPa value of the optimal variant being only the lowest of the range of 2.5-5.9 MPa achieved in this experiment.

This article presents discoveries and inventions from different periods of mankind, which played an important role in social and technological evolution. Thus, from the period of the Ancient World (prehistory - 400 AD), we present: the appearance of stone tools (which occurred in East Africa and belongs to the first hominids); pottery (appeared in 10500 BC); the development of metallurgy (began in the Middle East, around 6500 BC); the invention of the ox-drawn plow (which occurred around 4000 BC); the construction of the first pyramid in Egypt (2600 BC); the development of iron processing (as part of the development of metallurgy, it occurred around 1400 BC); modernization of papermaking technology (attributed to Tsai Lun, China, around 105 AD); Another historical period that we analyzed in terms of discoveries and innovations that revolutionized humanity was the Middle Ages (400 - 1500). Thus, from this period we presented the following discoveries and inventions: the discovery of the number zero (occurred in 520 and belongs to Indian mathematicians); woodcut printing (appeared in sixth century China); the first printed newspaper (year 700); the development of algebra (it belongs to the Greek mathematician Diophantos, 3rd century AD); gunpowder (it was discovered around 850); the establishment of the University of Bologna (made in 1088); The last period approached was the current one. From this period we presented the following discoveries: magnetism - a new form of electricity; devices controlled only by hand gestures.

The importance of the innovation process lies in its main functions, those of generating and leading to the conception and development of new processes and products, based on creativity. Hence the need of education for innovation. In this article we present, for a start, the main stages of an innovation process. Then, elements of innovation management, innovation strategies, innovation activities. We also present aspects regarding the financing of the innovation process and of the technology transfer. As results of the efficient application of these theoretical elements specific to an innovation process, we present the main elements of a patent (Invention Patent no. 107025/1993) of one of the authors. This patent, entitled "Burner" has gone through all stages, from conception to implementation in industry. This implementation took place in the former Special Steels Plant ok Targoviste (COST), in Electric Steel Mill no. 1 (OE1), with a good technological and economic efficiency

The trade (qualitative and quantitative level of trade) can promote the concept of sustainable development. The concept of Sustainable Development involves the implementation of theoretical and practical components for making decisions in any situation in which features a man-type medium, be it the environment, economic or social. The goals of sustainable development include the harmonization of the economic, social and environmental targets. This paper presents the main types of the correlations: Trade – Sustainable Development – Economic Crisis. The Sustainable Development (SD) concept is also analyzed in direct correlation with the Corporate Social Responsibility (CSR) concept. The SD concept involves the implementation of theoretical and practical components for making decisions in any situation in which a man-type medium, be it the environment, economic or social features. The Corporations (qualitative and quantitative level of trade) can promote the concept of sustainable development. The goals of sustainable development include the harmonization of the economic, social and environmental targets. This paper presents the main research on the main types of the correlations: Corporate Social Responsibility (including trade) – Sustainable Development – Economic Crisis.

We provide a class of separable II1 factors $M$ whose central sequence algebra is not the ‘tail’ algebra associated with any decreasing sequence of von Neumann subalgebras of $M$. This settles a question of McDuff [On residual sequences in a II1 factor, J. Lond. Math. Soc. (2) (1971), 273–280].

In the article we present certain criteria and management principles applicable to education and scientific research, in order to optimize these two important areas. We thoroughly presented management criteria such as: the methodological criterion, the economic criterion, the social criterion, the informational criterion, the organizational criterion, the functional criterion. Among the management principles we analyzed there are: the principle of the command unit, the principle of decision-making and the principle of the balance between centralization and decentralization.

This article presents the main elements specific to the evaluation of research and development and innovation activities: evaluation of scientific research activity; evaluation of the staff involved; valuation of tangible assets; valuation of intangible assets. Also, we present in the article the two ways of approaching the evaluation of research, development, innovation: macroeconomic approach; microeconomic approach. The comparative analysis is based on the management by results and the management by objectives in the field of research activities, development, and innovation. In this context, we present the economic-financial indicators used in the evaluation of the research, development, innovation: the rate of new sales; cost savings rate; revenues from research development innovation.

The goals of this paper are twofold. First, we generalize the result of Gaboriau and Lyons [GL07] to the setting of von Neumann's problem for equivalence relations, proving that for any non-amenable ergodic probability measure preserving (pmp) equivalence relation $\mathcal{R}$, the Bernoulli extension over a non-atomic base space $(K, \kappa)$ contains the orbit equivalence relation of a free ergodic pmp action of $\mathbb{F}_2$. Moreover, we provide conditions which imply that this holds for any non-trivial probability space $K$. Second, we use this result to prove that any non-amenable unimodular locally compact second countable group admits uncountably many free ergodic pmp actions which are pairwise not von Neumann equivalent (hence, pairwise not orbit equivalent).

We provide new examples of translation actions on locally compact groups with the “local spectral gap property” introduced in [5]. This property has applications to strong ergodicity, the Banach–Ruziewicz problem, orbit equivalence rigidity, and equidecomposable sets. The main group of study here is the group $\operatorname{Isom}\left (\mathbb{R}^{d}\right )$ of orientation-preserving isometries of the Euclidean space $\mathbb{R}^{d}$, for d ≥ 3. We prove that the translation action of a countable dense subgroup Γ on Isom$\left (\mathbb R^{d}\right )$ has local spectral gap, whenever the translation action of the rotation projection of Γ on SO(d) has spectral gap. Our proof relies on the amenability of $\operatorname{Isom}\left (\mathbb{R}^{d}\right )$ and on work of Lindenstrauss and Varjú [12].

We prove that if Γ is an icc irreducible lattice in a product of connected non-compact rank one simple Lie groups with finite center, then the II 1 {\mathrm{II}_{1}} factor L ⁢ ( Γ ) {L(\Gamma)} is prime. In particular, we deduce that the II 1 {\mathrm{II}_{1}} factors associated to the arithmetic groups PSL 2 ⁢ ( ℤ ⁢ [ d ] ) {\mathrm{PSL}_{2}(\mathbb{Z}[\sqrt{d}])} and PSL 2 ⁢ ( ℤ ⁢ [ S - 1 ] ) {\mathrm{PSL}_{2}(\mathbb{Z}[S^{-1}])} are prime for any square-free integer d ≥ 2 {d\geq 2} with d ≢ 1 ⁢ ( mod ⁡ 4 ) {d\not\equiv 1~{}(\operatorname{mod}\,4)} and any finite non-empty set of primes S. This provides the first examples of prime II 1 {\mathrm{II}_{1}} factors arising from lattices in higher rank semisimple Lie groups. More generally, we describe all tensor product decompositions of L ⁢ ( Γ ) {L(\Gamma)} for icc countable groups Γ that are measure equivalent to a product of non-elementary hyperbolic groups. In particular, we show that L ⁢ ( Γ ) {L(\Gamma)} is prime, unless Γ is a product of infinite groups, in which case we prove a unique prime factorization result for L ⁢ ( Γ ) {L(\Gamma)} .

We survey some of the progress made recently in the classification of von Neumann algebras arising from countable groups and their measure preserving actions on probability spaces. We emphasize results which provide classes of (W$^*$-superrigid) actions that can be completely recovered from their von Neumann algebras and II$_1$ factors that have a unique Cartan subalgebra. We also present cocycle superrigidity theorems and some of their applications to orbit equivalence. Finally, we discuss several recent rigidity results for von Neumann algebras associated to groups., submitted to Proc. of the ICM 2018

In this article we aim to create a software application aimed at highlighting the importance of the technical and economic estimate in making the bushings. This software was created as a web platform, available at: https://www.bucsa-sim.com, in order to maximize the accessibility, speed and efficiency of the complex process that underlies the construction of parts, in our case, bushings. The idea of developing this software started from the necessity generated by the fact that currently there is only one website on the Romanian market available at: https://bucsebronz.ro/calculator-piese/, which does not allow users to calculate the technical-economic estimate in real time, but only to send a simple form to the company. The use of this application is part of the new concept of Industrialization 4.0 because it allows operation in the cloud with immediate access to the display of the price of a bushing made of elements recovered from waste. Taking into consideration that materials such as copper and lead can come from recycling of batteries and accumulators, this application contributes to a better integration of the processing of these materials in the priciples or the circular economy.

The qualitative impact calculation for the implementation of a social economy project can be done using dedicated computing software. In this paper we have defined PQS which is an application on JAVA support that allows use irrespective of the existing support platform on the computer. The created application has the advantage that it can run both on computers and on other devices (tablets, phones, etc.). The input data are represented by the values assumed and realized in the project and are stored in a MySQL database.

We study the notion of permutation stability (or P-stability) for countable groups. Our main result provides a wide class of non-amenable product groups which are not P-stable. This class includes the product group Σ × Λ , whenever Σ admits a non-abelian free quotient and Λ admits an infinite cyclic quotient. In particular, we obtain that the groups F m × Z d and F m × F n are not P-stable, for any integers m , n ≥ 2 and d ≥ 1 . This implies that P-stability is not closed under the direct product construction, which answers a question of Becker, Lubotzky and Thom. The proof of our main result relies on a construction of asymptotic homomorphisms from Σ × Λ to finite symmetric groups starting from sequences of finite index subgroups in Σ and Λ with and without property (τ). Our method is sufficiently robust to show that the groups covered are not even flexibly P-stable, thus giving the first such non-amenable residually finite examples.

We provide a fairly large class of II $$_1$$ factors N such that $$M=N\bar{\otimes }R$$ has a unique McDuff decomposition, up to isomorphism, where R denotes the hyperfinite II $$_1$$ factor. This class includes all II $$_1$$ factors $$N=L^{\infty }(X)\rtimes \Gamma $$ associated to free ergodic probability measure preserving (p.m.p.) actions $$\Gamma \curvearrowright (X,\mu )$$ such that either (a) $$\Gamma $$ is a free group, $$\mathbb F_n$$ , for some $$n\ge 2$$ , or (b) $$\Gamma $$ is a non-inner amenable group and the orbit equivalence relation of the action $$\Gamma \curvearrowright (X,\mu )$$ satisfies a property introduced in Jones and Schmidt (Am J Math 109(1):91–114, 1987). On the other hand, settling a problem posed by Jones and Schmidt in 1985, we give the first examples of countable ergodic p.m.p. equivalence relations which do not satisfy the property of Jones and Schmidt (1987). We also prove that if $${\mathcal {R}}$$ is a countable strongly ergodic p.m.p. equivalence relation and $${\mathcal {T}}$$ is a hyperfinite ergodic p.m.p. equivalence relation, then $${\mathcal {R}}\times {\mathcal {T}}$$ has a unique stable decomposition, up to isomorphism. Finally, we provide new characterisations of property Gamma for II $$_1$$ factors and of strong ergodicity for countable p.m.p. equivalence relations.

The spatial organization of enterprises is of great importance for the metallic materials industry (metallurgy), given the diversity and complexity of the technological processes and the related equipment. In an enterprise from the metallic materials industry, there may be sections for: production, casting, forging, mechanical (hot and / or cold) processing, assembly etc. for the different stages of the technological process related to the products to be made. The article presents theoretical and practical elements regarding the management of the spatial organization of enterprises in the metallic materials industry. The principles and methods of spatial organization are presented and analyzed. These principles and methods are based on the biunivocal relation between the functional and constructive changes related to the technologies and equipment (machinery, aggregates) specific to the metallic material industry. Prescribing (establishing) the objective function (OF) of the technological processes modeling system in the metallic materials industry is based on the qualitative - economic analysis of these processes.

This article presents the main possibilities for steel refining in Ladle Furnace (LF). These, are presented: steelmaking stages, steel refining through argon bottom stirring, online control of the bottom stirring, bottom stirring diagram during LF treatment of a heat, porous plug influence over the argon stirring, bottom stirring porous plug, analysis of porous plugs disposal on ladle bottom surface, bottom stirring simulation with ANSYS, bottom stirring simulation with Autodesk CFD.

Let $\Gamma\curvearrowright (X,\mu)$ be a measure preserving action of a countable group $\Gamma$ on a standard probability space $(X,\mu)$. We prove that if the action $\Gamma\curvearrowright X$ is not profinite and satisfies a certain spectral gap condition, then there does not exist a countable-to-one Borel homomorphism from its orbit equivalence relation to the orbit equivalence relation of any modular action (i.e., an inverse limit of actions on countable sets). As a consequence, we show that if $\Gamma$ is a countable dense subgroup of a compact non-profinite group $G$ such that the left translation action $\Gamma\curvearrowright G$ has spectral gap, then $\Gamma\curvearrowright G$ is antimodular and not orbit equivalent to any, {\it not necessarily free}, profinite action. This provides the first such examples of compact actions, partially answering a question of Kechris and answering a question of Tsankov.

We give sufficient conditions, in terms of the existence of unbounded derivations satisfying certain properties, which ensure that a II$_1$ factor $M$ is prime or has at most one Cartan subalgebra. For instance, we prove that if there exists a real closable unbounded densely defined derivation $\delta:M\rightarrow L^2(M)\bar{\otimes}L^2(M)$ whose domain contains a non-amenability set, then $M$ is prime. If $\delta$ is moreover "algebraic" (i.e. its domain $M_0$ is finitely generated, $\delta(M_0)\subset M_0\otimes M_0$ and $\delta^*(1\otimes 1)\in M_0$), then we show that $M$ has no Cartan subalgebra. We also give several applications to examples from free probability. Finally, we provide a class of countable groups $\Gamma$, defined through the existence of an unbounded cocycle $b:\Gamma\rightarrow \mathbb C(\Gamma/\Lambda)$, for some subgroup $\Lambda

We study equivalence relations that arise from translation actions Γ ↷ G \Gamma\curvearrowright G which are associated to dense embeddings Γ < G \Gamma of countable groups into second countable locally compact groups. Assuming that G is simply connected and the action Γ ↷ G \Gamma\curvearrowright G is strongly ergodic, we prove that Γ ↷ G \Gamma\curvearrowright G is orbit equivalent to another such translation action Λ ↷ H \Lambda\curvearrowright H if and only if there exists an isomorphism δ : G → H \delta:G\to H such that δ ⁢ ( Γ ) = Λ \delta(\Gamma)=\Lambda . If G is moreover a real algebraic group, then we establish analogous rigidity results for the translation actions of Γ on homogeneous spaces of the form G / Σ G/\Sigma , where Σ < G \Sigma is either a discrete or an algebraic subgroup. We also prove that if G is simply connected and the action Γ ↷ G \Gamma\curvearrowright G has property (T), then any cocycle w : Γ × G → Λ w:\Gamma\times G\to\Lambda with values in a countable group Λ is cohomologous to a homomorphism δ : Γ → Λ \delta:\Gamma\to\Lambda . As a consequence, we deduce that the action Γ ↷ G \Gamma\curvearrowright G is orbit equivalent superrigid: any free nonsingular action Λ ↷ Y \Lambda\curvearrowright Y which is orbit equivalent to Γ ↷ G \Gamma\curvearrowright G , is necessarily conjugate to an induction of Γ ↷ G \Gamma\curvearrowright G .

We study Cartan subalgebras in the context of amalgamated free product II$_1$ factors and obtain several uniqueness and non-existence results. We prove that if $\Gamma$ belongs to a large class of amalgamated free product groups (which contains the free product of any two infinite groups) then any II$_1$ factor $L^{\infty}(X)\rtimes\Gamma$ arising from a free ergodic probability measure preserving action of $\Gamma$ has a unique Cartan subalgebra, up to unitary conjugacy. We also prove that if $\mathcal R=\mathcal R_1*\mathcal R_2$ is the free product of any two non-hyperfinite countable ergodic probability measure preserving equivalence relations, then the II$_1$ factor $L(\mathcal R)$ has a unique Cartan subalgebra, up to unitary conjugacy. Finally, we show that the free product $M=M_1*M_2$ of any two II$_1$ factors does not have a Cartan subalgebra. More generally, we prove that if $A\subset M$ is a diffuse amenable von Neumann subalgebra and $P\subset M$ denotes the algebra generated by its normalizer, then either $P$ is amenable, or a corner of $P$ embeds into $M_1$ or $M_2$., Comment: This new (and final) version of the paper includes an appendix written jointly with Stefaan Vaes which fixes a gap from the previous version

The criteria function concept consists of transforming the criteria function (CF) in a quality-economical matrix math MQE. The levels of prescribing the criteria function was obtained by using a composition algorithm for three vectors: T vector – technical parameters’ vector (ti); Ē vector – economical parameters’ vector (ej) and P vector – weight vector (p1). For each product or service, the area of the circle represents the value of its sales. The BCG Matrix thus offers a very useful map of the organization’s service strengths and weaknesses, at least in terms of current profitability, as well as the likely cash flows.

We prove that there exist uncountably many separable II$_1$ factors whose ultrapowers (with respect to arbitrary ultrafilters) are non-isomorphic. In fact, we prove that the families of non-isomorphic II$_1$ factors originally introduced by McDuff \cite{MD69a,MD69b} are such examples. This entails the existence of a continuum of non-elementarily equivalent II$_1$ factors, thus settling a well-known open problem in the continuous model theory of operator algebras., 16 pages

Our article presents possibilities of applying the concept Fuzzy Networks for an efficient metallurgical industry in Romania. We also present and analyze Fuzzy Networks complementary concepts, such as Expert Systems (ES), Enterprise Resource Planning (ERP), Analytics and Intelligent Strategies (SAI). The main results of our article are based on a case study of the possibilities of applying these concepts in metallurgy through Fuzzy Networks. Also, it is presented a case study on the application of the FUZZY concept on the Romanian metallurgical industry.

The paper presents a theoretical and experimental analysis of the polluting generating mechanisms for steel making in the Electric Arc Furnaces (EAF). The scheme for the environment’s polluting system through the EAF is designed and presented in this paper. The ecological experimenting consisted of determining by specialized measures of the dust percentage in the evacuated gases from the EAF and of thereof gas pollutants. From the point of view of reducing the impact on the environment, the main problem of the electric arc furnace (EAF) is the optimization of the powder collecting from the process gases, both from the furnace and from the work-area. The paper deals with the best dependence between the aggregate’s constructive, functional and technological factors, which are necessary for the furnace’s ecologization and for its energetically-technologically performances increasing.

Our article presents possibilities of applying the concept Fuzzy Networks for an efficient metallurgical industry in Romania. We also present and analyze Fuzzy Networks complementary concepts, such as Expert Systems (ES), Enterprise Resource Planning (ERP), Analytics and Intelligent Strategies (SAI). The main results of our article are based on a case study of the possibilities of applying these concepts in metallurgy through Fuzzy Networks. There are presented the domains afferent to KIBS are defined complying with the standardized classification of industrial sectors according to European Monitoring Centre on Change (EMCC). It is also analyze important approaches in the specific scientific literature, the research methodology a study case. KIBS concept implementation to the Romanian metallurgical industry aims also to include performance of activities concerning the formulation and development of new specific concepts.

Aluminum and aluminum alloy usage has a great economic and social importance. Therefore, so customary in our lives, aluminum and its alloys have a great spread in various fields. Our paper presents possibilities for optimization of aluminum (Al) alloys elaboration and casting processes by specific mathematical modeling. Some of these developments might include: developing new furnace types that will replace the largely exposed melt surface with a reduced surface area, thus improving energy consumption, environmental performance and overall efficiency through reduced metal loss; the development of in–line metal treatment units through high speed degassing. Direct and reliable detection and measurement techniques of non-metallic measurements will be developed; continuous production processes will replace sequential operations used to produce tin foil, extruded products and remelted alloyed ingots. We also present the main modeling principle and we describe the algorithm of modeling. Recycling provides a viable solution to existing shortages of raw materials. The use of products made with secondary aluminum provides high energy savings compared to the same products that use primary aluminum. Recycling aluminum products has a positive impact on the environment, its recyclability being preferred over other materials. An important principle of mathematical modeling is the principle of analogy. This principle consists in observing and analyzing competently the modeled reality, using both analogy with other fields of research and logical homology.

Highlighting the qualitative impact that the implementation of a social economy project generates is difficult to achieve, as we are talking about projects with a social impact for which the economic factor is not a priority one. Under these circumstances, the assessment of the quality of such an approach can be made taking into account long-term social implications, psychological implications, comfort and safety, etc. To quantify the activities and the impact on the quality of life, we can define a number of indicators to quantify these aspects. In order to quantify such an aspect, we have to consider mainly 2 categories of elements: target group and project indicators.

The concept of a scientific research project offer must be based on the analysis of the four types of resources: the human resources, the financial resources, the material resources and the informational resources. We note the importance of the human resource quality. In the following figure we present the main elements of the design algorithm of a research project. The feasibility study (otherwise very complex) is of great importance for the success and viability of the project. We have developed the algorithm for designing a scientific research project. Thus, we have devised several items, in a non-fortuitous order: formulation of the theme, resources analysis, feasibility study, offer formulation, project drawing, project implementation, project evaluation, dissemination. We have critically analyzed several definitions of a scientific research project. For example, “a set of investments and other planned activities to achieve specific objectives within a predetermined time frame and budget”, or, “a planned action that is a set of interrelated and coordinated activities to achieve specific objectives within a given budget and a period of determined time”. We also analyze the key functions of a scientific research project: specifying the issue to be addressed, specifying the objectives to be achieved, specifying the activities to be undertaken to achieve the objectives, specifying the revenue (or resources) needed for the deployment activities, identifying and specifying the responsibilities of the different organizations involved in implementation of the project, allowing technical and administrative reviews of the project, the basis for monitoring and evaluating the project that can be done either during the project’s implementation, or after the project has been completed. We have formulated in the article specific concepts on: “a development program is sustainable when it is able to provide an appropriate level of benefits over a longer period of time after the financial, managerial and technical assistance from the external donor ended”, or, “for most projects sustainability is a default, and donors and recipients wait and take responsibility that certain aspects of the activity will continue. Failure to make explicit sustainability as part of the project’s training and implementation process may lead to lack of benefit”.

The article presents specific aspects of management and models for economic analysis. Thus, we present the main types of economic analysis: statistical analysis, dynamic analysis, static analysis, mathematical analysis, psychological analysis. Also we present the main object of the analysis: the technological activity analysis of a company, the analysis of the production costs, the economic activity analysis of a company, the analysis of equipment, the analysis of labor productivity, the analysis of the goods flow.Keywords: Economic analysis, Models, Adoption of innovation

The four strategic directions (referring to the entire life cycle of aluminum) are as follows: production, primary use, recycling, and reuse. Thus, in this work, the following are analyzed and optimized: reducing greenhouse gas emissions from aluminum production, increasing energy efficiency in aluminum production, maximizing used-product collection, recycling, and reusing. According to the energetic balance at the gaseous environment level, the conductive transfer model is also analyzed through the finished elements method. Several principles of modeling and optimization are presented and analyzed: the principle of analogy, the principle of concepts, and the principle of hierarchization. Based on these principles, an original diagram model is designed together with the corresponding logic diagram. This article also presents and analyzes the main benefits of aluminum recycling and reuse. Recycling and reuse of aluminum have the main advantage that it requires only about 5% of energy consumed to produce it from bauxite. The aluminum recycling and production process causes the emission of pollutants such as dioxides and furans, hydrogen chloride, and particulate matter. To control these emissions, aluminum recyclers are required to comply with the National Emission Standards for Hazardous Air Pollutants for Secondary Aluminum Production. The results of technological, economic, and ecological optimization of aluminum recycling are based on the criteria function’s evaluation in the modeling system.

This paper presents an algorithmic analysis of the marketing mix in metallurgy. It also analyzes the main correlations and their optimizing possibilities through an efficient management. Thus, both the effect and the importance of the marketing mix, for components (the four “P-s”) areanalyzed in the materials’ industry, but their correlations as well, with the goal to optimize the specific management. There are briefly presented the main correlations between the 4 marketing mix components (the 4 “P-s”) for a product within the materials’ industry, including aspects regarding specific management.Keywords: Management Model, Materials Industry, Marketing Mix, Correlations.

This paper presents the main fundamental concepts concerning the methods of economic analysis: necessity of economic analysis, information system, types of economic analysis, methodologies used for the economic analysis of company, study of the factor which explain the results of the economic analysis of company, stage of the practical analysis. However in relation to conditions of economic crisis. In the same context is presented and analyzed the dictum of Nouriel Roubini, who said: “Stop austerity in the crisis!”. So, this paper analyzes “austerity vs crisis”,“insolvency - good or bad?” and “Sustainable Development” too.

We introduce a novel notion of local spectral gap for general, possibly infinite, measure preserving actions. We establish local spectral gap for the left translation action $$\Gamma \curvearrowright G$$ , whenever $$\Gamma $$ is a dense subgroup generated by algebraic elements of an arbitrary connected simple Lie group G. This extends to the non-compact setting works of Bourgain and Gamburd (Invent Math 171:83–121, 2008; J Eur Math Soc (JEMS) 14:1455–1511, 2012), and Benoist and de Saxce (Invent Math 205:337–361, 2016). We present several applications to the Banach–Ruziewicz problem, orbit equivalence rigidity, continuous and monotone expanders, and bounded random walks on G. In particular, we prove that, up to a multiplicative constant, the Haar measure is the unique $$\Gamma $$ -invariant finitely additive measure defined on all bounded measurable subsets of G.

Our article features the elements that make up the cost of production. The economic activity implies a consumption of factors followed-up by products expressed in goods or services. In the first part of the article, we have defined and detailed the cost of production. In the second part we have calculated the cost of the production of one tone of low alloyed steel with vanadium. The prices for the components of cost production have been established within, Tenaris site, located in Calarasi county, Romania.

Consider the following three properties for countable discrete groups G: (1) G has an infinite subgroup with relative property (T), (2) the group von Neumann algebra L(G) has a diffuse von Neumann subalgebra with relative property (T) and (3) G does not have Haagerup’s property. It is clear that (1) implies (2) and (2) implies (3). I will prove that both of the converses are false. This is joint work with Ionut Chifan.

We prove that if a countable group Γ contains a copy of F_2, then it admits uncountably many non orbit equivalent actions