Search results for: Arrow’s impossibility theorem

Authors: Saulius Minkevicius, Edvinas Greicius

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The paper is devoted to the analysis of queueing systems in the context of the network and communications theory. We investigate the inequality in an open queueing network and its applications to the theorems in heavy traffic conditions (fluid approximation, functional limit theorem, and law of the iterated logarithm) for a queue of customers in an open queueing network.

Keywords: fluid approximation, heavy traffic, models of information systems, open queueing network, queue length of customers, queueing theory

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Authors: Jin Sim, Kwan U. Kim, Ryong Jin Jang, Sung Duk Kim

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Earth rotation is one of astronomical phenomena without which it is impossible to think of human life. That is why the investigation of the Earth's rotation is very important, and it has a long history of study. Invention of quartz clocks in the 1930s and atomic time in the 1950s and introduction of modern technology into astronomic observation in recent years resulted in rapid development of the study of Earth’s rotation. The theory of the Earth rotation, however, has not been up to the high level of astronomic observation due to limitation of the time such as the impossibility of quantitative calculation of moment of external force for Euler’s dynamical equation based on Newtoniam mechanics. As a typical example, we can take the problems that cover the instabilities of the Earth’s rotation proved completely by the astronomic observations as well as polar motion, the precession and nutation of the Earth rotation axis, which have not been described in a single equation in a quantitative way from the unique law of the Earth rotation. In particular, at present, the problem of what the main factor causing the instabilities of the Earth rotation is has not been solved clearly in quantitative ways yet. Therefore, this paper addresses a quantitative proof that the main factor which causes the instabilities of the Earth rotation is the moment of external force rather than variations in the relative atmospheric angular momentum and in moment of inertia of the Earth’s body due to the time limitation and under some assumptions. Then the future direction of research is proposed.

Keywords: atmospheric angular momentum, instabilities of the Earth’s rotation, law of the Earth’s rotation change, moment of inertia of the Earth

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Authors: Sojung Kim

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This paper explores how the Partition of Korea is absorbed into everyday life through North Korean migrant women’s rituals for traditional holidays in Korea. In national holidays called myungjul, Koreans traditionally visit their paternal ancestor’s hometowns to hold jesa, the rites for the ancestors, at the graves and home. Due to the physical gaps in the kinship networks, marked by the kin left behind in North Korea, North Korean migrants gather among themselves in the neighborhood in South Korea as if they make the myungjul ritual of the family gatherings. This impossibility of the proper practice of the rites insinuates the violence of the Partition refracted into the family relations between those in the South and those in the North. Yet, the myungjul gathering creates a kind of collective hometown, beside one’s genealogical hometown, where they can express lamentation and guilt over not being able to visit their parents and ancestors in their hometowns, which they are traditionally required to do. In this as-if ritual, myungjul is re-created for and by the women and for others in the community. Yet, the texture of this ritual is marked by discontent and dissatisfaction. Attending to fostering discontents that seep into the collective events, this paper aims to seek ways to study the violence that permeated in everyday life in partitioned Korea.

Keywords: as-if ritual, everyday life, kinship, migration

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Authors: Song Ni, Junxiang Xu

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This paper concerns quasi-periodic perturbations with parameters of 2-dimensional degenerate systems. If the equilibrium point of the unperturbed system is elliptic-type degenerate. Assume that the perturbation is real analytic quasi-periodic with diophantine frequency. Without imposing any assumption on the perturbation, we can use a path of equilibrium points to tackle with the Melnikov non-resonance condition, then by the Leray-Schauder Continuation Theorem and the Kolmogorov-Arnold-Moser technique, it is proved that the equation has a small response solution for many sufficiently small parameters.

Keywords: quasi-periodic systems, KAM-iteration, degenerate equilibrium point, response solution

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Authors: Ananya G., B. Varshitha, Shwetha S., Kavitha S. N., Praveen Kumar Gupta

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Teleportation is the ability to travel by just reappearing at some other spot. Though teleportation has never been achieved, quantum teleportation is possible. Quantum teleportation is a process of transferring the quantum state of a particle onto another particle, under the circumstance that one does not get to know any information about the state in the process of transformation. This paper presents a brief overview of quantum teleportation, discussing the topics like Entanglement, EPR Paradox, Bell's Theorem, Qubits, elements for a successful teleport, some examples of advanced teleportation systems (also covers few ongoing experiments), applications (that includes quantum cryptography), and the current hurdles for future scientists interested in this field. Finally, major advantages and limitations to the existing teleportation theory are discussed.

Keywords: teleportation, quantum teleportation, quantum entanglement, qubits, EPR paradox, bell states, quantum particles, spooky action at a distance

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Authors: Hassan J. Al Salman, Ahmed A. Al Ghafli

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In this study, we consider a nonlinear in time finite element approximation of a reaction diffusion system of lambda-omega type. We use a fixed-point theorem to prove existence of the approximations at each time level. Then, we derive some essential stability estimates and discuss the uniqueness of the approximations. In addition, we employ Nochetto mathematical framework to prove an optimal error bound in time for d= 1, 2 and 3 space dimensions. Finally, we present some numerical experiments to verify the obtained theoretical results.

Keywords: reaction diffusion system, finite element approximation, stability estimates, error bound

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Authors: Ying Yi Wu

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In this paper, we present a proof of the fact that a finite morphism is proper. We show that a finite morphism is universally closed and of finite type, which are the conditions for properness. Our proof is based on the theory of schemes and involves the use of the projection formula and the base change theorem. We first show that a finite morphism is of finite type and then proceed to show that it is universally closed. We use the fact that a finite morphism is also an affine morphism, which allows us to use the theory of coherent sheaves and their modules. We then show that the map induced by a finite morphism is flat and that the module it induces is of finite type. We use these facts to show that a finite morphism is universally closed. Our proof is constructive, and we provide details for each step of the argument.

Keywords: finite, morphism, schemes, projection.

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Authors: K. Vigneshwaran, Manoj Pandey

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In this paper, breathing crack is considered for the non linear dynamic analysis. The stiffness of the cracked beam is found out by using influence coefficients. The influence coefficients are calculated by using Castigliano’s theorem and strain energy release rate (SERR). The equation of motion of the beam was derived by using Hamilton’s principle. The stiffness and natural frequencies for the cracked beam has been calculated using XFEM and Eigen approach. It is seen that due to presence of cracks, the stiffness and natural frequency changes. The mode shapes and the FRF for the uncracked and breathing cracked cantilever beam also obtained and compared.

Keywords: breathing crack, XFEM, mode shape, FRF, non linear analysis

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

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In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: conservation laws, diffusion equations, Cahn-Hilliard equations, evolving surfaces

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Authors: P. K. Rahul Krishna, S. Sandeep Kumar, Jayanthi Sunder Raj

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The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

Keywords: arithmetic progression, hypotenuse leg difference method, natural numbers, Pythagorean triplets, quadratic equation

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Authors: Zhifu Li, Lei Li, Wanting Zhou, Yuanhang He

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This paper proposed a lightweight certificate-less authentication and key exchange protocol (Light-CL-PKC) based on elliptic curve cryptography and the Chinese Remainder Theorem for smart home scenarios. Light-CL-PKC can efficiently reduce the computational cost of both sides of authentication by forgoing time-consuming bilinear pair operations and making full use of point-addition and point-multiplication operations on elliptic curves. The authentication and key exchange processes in this system are also completed in a a single round of communication between the two parties. The analysis result demonstrates that it can significantly minimize the communication overhead of more than 32.14% compared with the referenced protocols, while the runtime for both authentication and key exchange have also been significantly reduced.

Keywords: authentication, key exchange, certificateless public key cryptography, elliptic curve cryptography

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Authors: Leonard Kabeya Mukeba Yakasham

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The theoretical machinery from singularity theory introduced by Glolubitsky, Stewart, and Schaeffer, to study equivariant bifurcation problem is completed and expanded wile generalized to the multiparameter context. In this setting the finite deterinancy theorem or normal forms, the stability of equivariant bifurcation problem, and the structural stability of universal unfolding are discussed. With Yakam Matrix the solutions are limited for some partial differential equations stochastic nonlinear of the open questions in singularity artificial intelligence for future.

Keywords: equivariant bifurcation, symmetry singularity, equivariant jets and transversality, normal forms, universal unfolding instability, structural stability

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Authors: Anandhi Santhosh

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In order to describe various real-world problems in physical and engineering sciences subject to abrupt changes at certain instants during the evolution process, impulsive differential equations has been used to describe the system model. In this article, the problem of approximate controllability for nonlinear impulsive integrodifferential equations with state-dependent delay is investigated. We study the approximate controllability for nonlinear impulsive integrodifferential system under the assumption that the corresponding linear control system is approximately controllable. Using methods of functional analysis and semigroup theory, sufficient conditions are formulated and proved. Finally, an example is provided to illustrate the proposed theory.

Keywords: approximate controllability, impulsive differential system, fixed point theorem, state-dependent delay

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Authors: Laskri Yamina, Rehouma Abdel Hamid

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In this paper we present a new class named polar of monic orthogonal polynomials with respect to the area measure supported on G, where G is a bounded simply-connected domain in the complex planeℂ. We analyze some open questions and discuss some ideas properties related to solving asymptotic behavior of polar Bergman polynomials over domains with corners and asymptotic behavior of modified Bergman polynomials by affine transforms in variable and polar modified Bergman polynomials by affine transforms in variable. We show that uniform asymptotic of Bergman polynomials over domains with corners and by Pritsker's theorem imply uniform asymptotic for all their derivatives.

Keywords: Bergman orthogonal polynomials, polar rthogonal polynomials, asymptotic behavior, Faber polynomials

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Authors: Wieslaw Marszalek, Zdzislaw Trzaska

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Interesting properties of various one-period loops of singularly perturbed memristive circuits with mixed-mode oscillations (MMOs) are analyzed in this paper. The analysis is mixed, both analytical and numerical and focused on the properties of pinched hysteresis of the memristive element and other one-period loops formed by pairs of time-series solutions for various circuits' variables. The memristive element is the only nonlinear element in the two circuits. A theorem on periods of mixed-mode oscillations of the circuits is formulated and proved. Replacements of memristors by parallel G-C or series R-L circuits for a MMO response with equivalent RMS values is also discussed.

Keywords: mixed-mode oscillations, memristive circuits, pinched hysteresis, one-period loops, singularly perturbed circuits

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Authors: Talita Cavaignac

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Adorno's critique of totality, especially in a split society marked by reification, also rests on the impossibility of generalizing normative principles. Given the unfeasibility of normative universalizations, which conditions can justify the possibility of criticism and normativity in Adorno's thought? If reason itself is still entangled in alienation from the model of the domination of nature, how could be possible a critical theory? In political terms, if the notion of totality is challenged by the critique of identity, how can Adorno maintain the ideal of liberation and reconciliation between private interests and the possibility of some sort of ethics without giving up a materialist theory of society and without betting in a necessary link between redemption and history? Faced with this complex of questions, it is intended to reflect on the sense in which the notion of ‘suffering’ could throw help to the epistemological problem of the foundations of criticism in Adorno's work. The idea is that, in contrast to a universalizable model of justice, Adorno mobilizes in the notion of ‘suffering’ a gateway to the critical reflection of society. He would thus develop an approach to moral problems through the sensual-bodily perspective, fear, pain, and somatic factors. Nevertheless, due to the attention to the damaged experience and to the constitution of subjectivity -a sense in which the concept of mimesis continues to stand out- we understand suffering as an expression of an objective reification. Following the statement of other authors, the intention is to think how the resources linked to the idea of ‘suffering’ in Adorno's writings are engaged in the reflection of the problem of morality and of the contradictions between universal and particular (articulated in Hegel's tradition).

Keywords: ethics, morality, sensitive, Theodor Adorno

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Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma

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An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

Keywords: Black-Scholes partial differential equations, Ito process, option price valuation, partial differential equations

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Authors: Mohammad Naser Aldeen

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This study explores environmental justice issues among Bedouin communities in Israel’s Negev region, focusing on energy access and their exclusion from state-supported energy services. As a historically marginalized and indigenous population, Bedouins face intersecting inequities, including limited access to national grid energy, waste management, access to water, systematic discrimination, and environmental harms such as industrial pollution and land degradation. Employing Pellow’s Critical Environmental Justice framework, this research examines how power relations and intersecting identities – ethnicity, class, and indigeneity – shape energy exclusion. Utilizing K. Arrow’s Barriers Analysis framework, it identifies the multifaceted barriers obstructing equitable energy access, including structural policy deficiencies, socio-economic constraints, and administrative neglect. The study also highlights Bedouins’ resilience, advocacy, and community-led strategies to address these challenges through the adoption of solar energy. A mixed-methods approach integrates quantitative data with qualitative narratives from community leaders, policymakers, and activists, revealing the multidimensional nature of energy inequities in the Negev. Findings emphasize the urgent need for inclusive energy policies that address intersectional barriers and prioritize environmental justice in planning and management. By advancing discourse on energy equity, this research underscores the importance of integrating marginalized communities into sustainable energy systems, contributing to the development of equitable energy policies and fostering pathways toward environmental justice and sustainable development.

Keywords: environmental justice, energy justice, intersectionality, Bedouin communities, barriers analysis

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Authors: Xia Yang, Zheng Yang, Haiyong Sun, Yan Fang, Jingyu Liu, Jia Song

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The smart contract in Ethereum is a unique program deployed on the Ethereum Virtual Machine (EVM) to help manage cryptocurrency. The security of this smart contract is critical to Ethereum’s operation and highly sensitive. In this paper, we present a formal model for smart contract, using the separated term-obligation (STO) strategy to formalize and verify the smart contract. We use the IBM smart sponsor contract (SSC) as an example to elaborate the detail of the formalizing process. We also propose a formal smart sponsor contract model (FSSCM) and verify SSC’s security properties with an interactive theorem prover Coq. We found the 'Unchecked-Send' vulnerability in the SSC, using our formal model and verification method. Finally, we demonstrate how we can formalize and verify other smart contracts with this approach, and our work indicates that this formal verification can effectively verify the correctness and security of smart contracts.

Keywords: smart contract, formal verification, Ethereum, Coq

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Authors: Vijay Kumar Kukreja, Ravneet Kaur

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In this paper, one dimensional advection diffusion model is analyzed using finite difference method based on Crank-Nicolson scheme. A practical problem of filter cake washing of chemical engineering is analyzed. The model is converted into dimensionless form. For the grid Ω × ω = [0, 1] × [0, T], the Crank-Nicolson spatial derivative scheme is used in space domain and forward difference scheme is used in time domain. The scheme is found to be unconditionally convergent, stable, first order accurate in time and second order accurate in space domain. For a test problem, numerical results are compared with the analytical ones for different values of parameter.

Keywords: Crank-Nicolson scheme, Lax-Richtmyer theorem, stability, consistency, Peclet number, Greschgorin circle

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Authors: Anisa Luli, Alessandra Santona

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Wanting a child and experiencing the impossibility to conceive is a painful condition that often is linked to infertility and often leads infertile individuals to experience psychological, relational and social problems. In this situation, infertile couples have to review their choices and take into consideration new ones. Few studies have focused on the decision-making style used by infertile individuals to solve their problem and on the factors that influences it. The aim of this paper is to define the style of decision-making used by infertile persons to give a solution to the “problem” and the predictive role of the attachment, of the representations of the relationship with parents in childhood and of the dyadic adjustment. The total sample is composed by 251 participants, divided in two groups: the experimental group composed by 114 participants, 62 males and 52 females, age between 25 and 59 years, and the control group composed by 137 participants, 65 males and 72 females, age between 22 and 49 years. The battery of instruments comprises: General Decision Making Style (GDMS), Experiences in Close Relationships Questionnaire Revised (ECR-R), Dyadic Adjustment Scale (DAS), Parental Bonding Instrument (PBI) and Symptom Checklist-90-R (SCL-90-R). The results from the analysis of the samples showed a prevalence of the rational decision-making style for both males and females, experimental and control group. There have been founded significant statistical relationships between the attachment scales, the representations of the parenting style, the dyadic adjustment and the decision-making styles. These results contribute to enrich the literature on the subject of decision-making in infertile people and show the relationship between the attachment and decision-making styles, confirming the few results in literature.

Keywords: attachment, decision-making style, infertility, dyadic adjustment

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Authors: František Včelař, Zuzana Pátíková

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Recently a new type of very general relational structures, the so called (L-)complete propelattices, was introduced. These significantly generalize complete lattices and completely lattice L-ordered sets, because they do not assume the technically very strong property of transitivity. For these structures also the main part of the original Tarski’s fixed point theorem holds for (L-fuzzy) isotone maps, i.e., the part which concerns the existence of fixed points and the structure of their set. In this paper, fundamental properties of (L-)complete propelattices are recalled and the so called L-fuzzy relatively isotone maps are introduced. For these maps it is proved that they also have fixed points in L-complete propelattices, even if their set does not have to be of an awaited analogous structure of a complete propelattice.

Keywords: fixed point, L-complete propelattice, L-fuzzy (relatively) isotone map, residuated lattice, transitivity

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Authors: Saimir Heta, Rialda Xhizdari, Kers Kapaj, Ilma Robo

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Background: The interests of both individuals involved, both the dentist with his professionalism, and the patient who claims and expects the proper professional dental service, are determined in cases of dental malpractice. The latter is a phenomenon that is also wearing the "cloak" of bilateral manipulations, which in themselves require strong legal control to regulate the relations between the involved parties. The two individuals are involved both individually and even professionally and emotionally, with support in the "ultimate" interests of the two people, which in the case of conflicts or grievances, which as a result are transported to the family or society of the affected individual. Main text: The reason for malpractice is the most difficult part to find and then to interpret. It can be professional in the view of "so much I know how to do, so much done", or in the view of the impossibility of individual health conditions to achieve high professional expectations. But, the reason can also be individual with the intention of doing bad without reason or with the source of an unhealthy mind and the source of malicious thinking. The professional himself is a human being and as such may be under the effect of individual treatments or vices, therefore causing misuse, a case that must be distinguished from intentional misuse and which must be judged for the results or damages caused by the professional based on criminal law. Conclusions: Malpractice in some cases may be unavoidable, beyond the good intention of the dental intervention, which should be well understood by both parties involved in this relationship. Malpractice is not necessarily related only to difficult clinical cases, but sometimes also appears as a random deviation of a dental treatment with a welldefined professional protocol. The legal support in the interpretation of malpractice cases should be much more specific according to previous cases, this practice specifically, perhaps also according to different religious states.

Keywords: dental ethics, malpractice, professional dental service, legal support

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Authors: Sabri Arik

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In this paper, we study the global asymptotic robust stability of delayed neural networks with norm-bounded uncertainties. By employing the Lyapunov stability theory and Homeomorphic mapping theorem, we derive some new types of sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slopebounded activation functions. An important aspect of our results is their low computational complexity as the reported results can be verified by checking some properties symmetric matrices associated with the uncertainty sets of network parameters. The obtained results are shown to be generalization of some of the previously published corresponding results. Some comparative numerical examples are also constructed to compare our results with some closely related existing literature results.

Keywords: neural networks, delayed systems, lyapunov functionals, stability analysis

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Authors: Michele Aleandri, Matteo Colangeli, Davide Gabrielli

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We study a generalization to a continuous setting of the classical Markov chain tree theorem. In particular, we consider an irreducible diffusion process on a metric graph. The unique invariant measure has an atomic component on the vertices and an absolutely continuous part on the edges. We show that the corresponding density at x can be represented by a normalized superposition of the weights associated to metric arborescences oriented toward the point x. A metric arborescence is a metric tree oriented towards its root. The weight of each oriented metric arborescence is obtained by the product of the exponential of integrals of the form ∫a/b², where b is the drift and σ² is the diffusion coefficient, along the oriented edges, for a weight for each node determined by the local orientation of the arborescence around the node and for the inverse of the diffusion coefficient at x. The metric arborescences are obtained by cutting the original metric graph along some edges.

Keywords: diffusion processes, metric graphs, invariant measure, reversibility

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Authors: Mariam Shah

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Stereotypes are not generally considered to be an acceptable influence upon any decision making process, particularly those involving judicial decision making outcomes. Yet, we are confronted with an uncomfortable truth that stereotypes may be operating to influence judicial outcomes. Variances in sentencing outcomes are not easily explained away by criminological, psychological, or sociological theorem, but may be answered via qualitative research produced within the field of phenomenology. This paper will examine the current literature pertaining to the effect of stereotypes on the criminal justice system within the UK, and will also discuss what the implications are for stereotypical influences upon decision making in the criminal justice system. This paper will give particular focus to shoplifting offences dealt with in UK criminal courts, but this research has long reaching implications for the criminal process more generally.

Keywords: decision making, judicial decision making, phenomenology, shoplifting, stereotypes

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Authors: Kajingulu Malandala, Ranganai Edmore

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The asymmetric Laplace distribution (ADL) is commonly used as the likelihood function of the Bayesian quantile regression, and it offers different families of likelihood method for quantile regression. Notwithstanding their popularity and practicality, ADL is not smooth and thus making it difficult to maximize its likelihood. Furthermore, Bayesian inference is time consuming and the selection of likelihood may mislead the inference, as the Bayes theorem does not automatically establish the posterior inference. Furthermore, ADL does not account for greater skewness and Kurtosis. This paper develops a new aspect of quantile regression approach for count data based on inverse of the cumulative density function of the Poisson, binomial and Delaporte distributions using the integrated nested Laplace Approximations. Our result validates the benefit of using the integrated nested Laplace Approximations and support the approach for count data.

Keywords: quantile regression, Delaporte distribution, count data, integrated nested Laplace approximation

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Authors: Saule Mussabekova

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Forensic investigation of human teeth plays an important role in detection of crime, particularly in cases of personal identification of dead bodies changed by putrefactive processes or skeletonized bodies as well as when finding bodies of unknown persons. 152 teeth have been investigated; 85 of them belonged to men and 67 belonged to women taken from alive people of different age. Teeth have been investigated after extraction. Two types of teeth have been investigated: teeth without integrity violation of dental crown and teeth with different degrees of its violation. Additionally, 517 teeth have been investigated that were collected from dead bodies, 252 of which belonged to women and 265 belonged to men, whatever the cause of death with death limitation from 1 month to 20 years. Isohemagglutinating serums and Coliclons of different series have been used for the research of tooth-group specificity by serological methods according to the AB0 system. Standard protocols of different techniques have been used for DNA purification from teeth (by reagent Chelex 100 produced by Bio-Rad using reagent kit 'DNA IQTM System' produced by Promega company (USA) and using columns 'QIAamp DNA Investigator Kit' produced by Qiagen company). Results of comparative forensic investigation of human teeth using serological and molecular genetic methods have shown that use of serological methods for forensic identification is sensible only in cases of preselection prior to the next molecular genetic investigation as well as in cases of impossibility of corresponding genetic investigation for different objective reasons. A number of advantages of methods of molecular genetics in the dental investigation have been marked, particularly in putrefactive changes, in personal identification. Key moments of modern condition of personal identification have been reflected according to dental state. Prospective directions of advance preparation of material have been emphasized for identification of teeth in forensic practice.

Keywords: dental state, forensic identification, molecular genetic analysis, teeth

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Authors: Josef Slapal

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Digital images are approximations of real ones and, therefore, to be able to study them, we need the digital plane Z2 to be equipped with a convenient structure that behaves analogously to the Euclidean topology on the real plane. In particular, it is required that such a structure allows for a digital analogue of the Jordan curve theorem. We introduce certain adjacency graphs on the digital plane and prove digital Jordan curves for them thus showing that the graphs provide convenient structures on Z2 for the study and processing of digital images. Further convenient structures including the wellknown Khalimsky and Marcus-Wyse adjacency graphs may be obtained as quotients of the graphs introduced. Since digital Jordan curves represent borders of objects in digital images, the adjacency graphs discussed may be used as background structures on the digital plane for solving the problems of digital image processing that are closely related to borders like border detection, contour filling, pattern recognition, thinning, etc.

Keywords: digital plane, adjacency graph, Jordan curve, quotient adjacency

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Authors: Marko Kolakovic

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Creative industries are an important sector of growth and development of knowledge economies. They have a positive impact on employment, economic growth, export and the quality of life in the areas where they are developed. Creative sectors include architecture, design, advertising, publishing, music, film, television and radio, video games, visual and performing arts and heritage. Following the positive trends of development of creative industries on the global and European level, this paper analyzes creative industries in general and specific characteristics of creative entrepreneurship. Special focus in this paper is put on the influence of the information communication technology on the development of new creative business models and protection of the intellectual property rights. One part of the paper is oriented on the analysis of the status of creative industries and creative entrepreneurship in Croatia. The main objective of the paper is by using the statistical analysis of creative industries in Croatia and information gained during the interviews with entrepreneurs, to make conclusions about potentials and development of creative industries in Croatia. Creative industries in Croatia are at the beginning of their development and growth strategy still does not exist at the national level. Statistical analysis pointed out that in 2015 creative enterprises made 9% of all enterprises in Croatia, employed 5,5% of employed people and their share in GDP was 4,01%. Croatian creative entrepreneurs are building competitive advantage using their creative resources and creating specific business models. The main obstacles they meet are lack of business experience and impossibility of focusing on the creative activities only. In their business, they use digital technologies and are focused on export. The conclusion is that creative industries in Croatia have development potential, but it is necessary to take adequate measures to use this potential in a right way.

Keywords: creative entrepreneurship, knowledge economy, business models, intellectual property

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