A Previously Unpublished Solution to Erlang's "Problem of Extinction of Families" by Carl Marius Christensen

I will survey a body of work, developed over the past decade or so, on algorithms for, and the computational complexity of, analyzing and model checking some important families of countably infinite-state Markov chains, Markov decision processes (MDPs), and stochastic games. These models arise by adding natural forms of recursion, branching, or a counter, to finite-state models, and they correspond to probabilistic/control/game extensions of classic automata-theoretic models like pushdown automata, context-free grammars, and one-counter automata. They subsume some classic stochastic processes such as multi-type branching processes and quasibirth-death processes. They also provide a natural model for probabilistic procedural programs with recursion.Some of the key algorithmic advances for analyzing these models have come from algorithms for computing the least fixed point (and greatest fixed point) solution for corresponding monotone systems of nonlinear (min/max)-polynomial equations. Such equations provide, for example, the Bellman optimality equations for optimal extinction and reachability probabilities for branching MDPs (BMDPs). A key role in these algorithms is played by Newton's method, and by a generalization of Newton's method which is applicable to the Bellman equations for BMDPs, and which uses linear programming in each iteration.By now, polynomial time algorithms have been developed for some of the key problems in this domain, while other problems have been shown to have high complexity, or to even be undecidable. Yet many algorithmic questions about these models remain open. I will highlight some of the open questions.(This talk partly describes joint work with Alistair Stewart and Mihalis Yannakakis.)

Researchers in education for sustainable development have argued that sustainability is not fixed but socially constructed, and that sustainability issues should be represented as a continuous quest rather than indisputable targets that can be anticipated, planned and regulated according to predetermined guidelines. These scholars often doubt that there is one ‘right’ way to be sustainable. Considering the immensity of environmental sustainability challenges, such as climate change, species extinction, and pollution, this article takes a different perspective. The author will argue that without acceptance of unsustainability as a concrete challenge that requires concrete positivistic solutions, the challenge of addressing unsustainable practices becomes unsurmountable. The author will argue that there is a need for clear articulation of 1. What (un)sustainability is; and 2. What the key challenges and causes of (un)sustainability are; and 3. How the sustainability challenges can be meaningfully addressed. This article will outline a number of helpful frameworks that address obstacles to sustainability, ranging from population growth to unsustainable production and consumption practices. In particular, these solutions include investment in family planning policies to counter the effects of overpopulation, and alternative production frameworks, such as Cradle to Cradle, The Blue Economy and Circular Economy that differ from the conventional frameworks such as eco-efficiency, and have the potential to move the quest for sustainability beyond ‘business as usual’. This article will conclude with the broader reflection that without goaloriented critical learning explicitly providing alternative sound models of sustainability, democratic learning may never permit transcendence from unsustainable models. In order to overcome the practical impasse inherent in much of neoliberal education, educators can begin to close ranks and realize that each has valuable strengths that can help in the reconstruction of education for sustainability.

Background: Current statistics indicate a concern for the mental health and psychological well-being of Tongan youth in New Zealand and Australia. This impacts on their social and educational functioning and drives ongoing inequalities. Such data pleads for research which identifies potential solutions that are effective for Tongan youth addressing the issue of their mental health. The current thesis aims to build knowledge about underlying factors that may contribute to the adverse outcomes of Tongan youth living in New Zealand and Australia. Compared to the Pacific Island and the general New Zealand youth, Tongan youth have had the highest rate of suicide; highest rate of suicidal thoughts and highest rate of suicide attempts in New Zealand. Tongan youth also have poor educational attainment and are over represented in the criminal justice system. Pressures around adapting to a host country with differing family and cultural values are proposed to contribute to the complexities of life for Tongan youth. In order to understand the well-being of young Tongans, it is essential to take account of the impact of migration on them and their families. This thesis utilised a socio-cultural lens of acculturation gaps to explore how family and school related factors contribute to the compromised outcomes of Tongan youth in New Zealand and Australia. Methods: This study consisted of one hundred Tongan mother-youth dyads from New Zealand and Australia. The study utilised standardised measures of acculturation and enculturation, youth problems, family and school-related factors and substance use. The questionnaires were available in both the Tongan and English language. Results: High rates of psychological problems were reported. Twenty two percent of youth were in the clinical category for internalising problems, 29% in the clinical category for externalising problems and 45% in the clinical category for total problems. New Zealand Tongan youth compared to Australian Tongan youth were significantly higher in the clinical category for externalising problems but significantly lower in the clinical category for total problems. Notably, youth reported low levels of substance use when compared to national data. There were significant differences between mothers and youth on measures of acculturation. Typically mothers reported higher levels of enculturation (i.e., retained Tongan cultural values) compared to youth while youth reported higher levels of acculturation (i.e., adopting host cultural values). Acculturation and enculturation gaps did not directly predict youth outcomes on either externalising or internalising problems. However, family conflict mediated the relationship between acculturation gap and youth outcomes (both internalising and externalising problems). Furthermore, low commitment to school moderated the mediation of family conflict on acculturation gap and externalising problems. Conclusion: The outcomes of New Zealand Tongan and Australian Tongan youth warrant concern and intervention. The implications of these findings inform and equip policy makers and service providers to educate and facilitate Tongan families and communities, to improve the health and well-being of Tongan youth in New Zealand and Australia.

Based on the current situation of families' finance management in the minority regions with China's relatively high inflation, this paper studies the problems of Chinese families' finance management in the minority regions and its solutions, in order to make it more scientific, reasonable and improve minorities' quality of life. By the use of logical reasoning, this article puts forward corresponding solutions for the problems. Implementing these solutions is helpful to reduce the gap between income brought by families' finance management in the minority regions and other areas, realize common prosperity and construct harmonious society.

Reactive flows are ubiquitous in several energy systems: internal combustion engines, industrial burners, gas turbine combustors. Numerical modeling of reactive flows is a key tool for the development of such systems. However, computational combustion is a challenging task per se. It generally includes different coupled physical and chemical processes. A single model can come to deal with simultaneous processes: turbulent mixing, multi-phase fluid-dynamics, radiative heat transfer, and chemical kinetics. It is required not only of mathematically representing these processes and coupling them to each other, but also of being numerical efficient. In some applications, the numerical model needs to be able to deal with different length scales. For instance, a continuum approach to reactive flows in porous media burners is not adequate: processes occurring at the pore-scale are not taken into account properly. It is therefore fundamental to have numerical methods able to capture phenomena at the microscopic scales and incorporate the effects in the macroscopic scale. The lattice Boltzmann method (LBM), a relatively new numerical method in computational fluid-dynamics (CFD), summarizes the requirements of numerical efficiency and potential to relate micro-and macro-scale. However, despite these features and the recent developments, application of LBM to combustion problems is limited and hence further improvements are required. In this thesis, we explore the suitability of LBM for combustion problems and extend its capabilities. The first key-issue in modeling reactive flows is represented by the fact that the model has to be able to handle the significant density and temperature changes that are tipically encountered in combustion. A recently proposed LBM model for compressible thermal flows is extended to simulate reactive flows at the low Mach number regime. This thermal model is coupled with the mass conservation equations of the chemical species. Also in this case a model able to deal with compressibility effects is derived. To this purpose, we propose a new scheme for solving the reaction-diffusion equations of chemical species where compressibility is accounted for by simply modifying the equilibrium distribution function and the relaxation frequency of models already available in the literature. This extension enables one to apply LBM to a wide range of combustion phenomena, which were not properly adressed so far. The effectiveness of this approach is proved by simulating combustion of hydrogen/air mixtures in a mesoscale channel. Validation against reference numerical solution in the continuum limit are also presented. An adequate treatment of thermal radiation is important to develop a mathematical model of combustion systems. In fact, combustion incorporates also radiation process, which tends to plays a significant role if high temperatures (and solid opaque particles) are involved. In the thesis a LBM model for radiation is presented. The scheme is derived from the radiative transfer equation for a participating medium, assuming isotropic scattering and radiative equilibrium condition. The azimuthal angle is discretized according to the lattice velocities on the computational plane, whereas an additional component of the discrete velocity normal to the plane is introduced to discretize the polar angle. The radiative LBM is used to solve a two-dimensional square enclosure bechmark problem. Validation of the model is carried out by investigating the effects of the spatial and angular discretizations and extinction coefficient on the solution. To this purpose, LBM results are compared against reference solutions obtained by means of standard Finite Volume Method (FVM). Extensive error analysis and the order of convergence of the scheme are also reported in the thesis. In order to extend the capabilities of LBM and make it more efficient in the simulation of reactive flows, in this thesis a new formulation is presented, referred to as Link-wise Artificial Compressibility Method (LW-ACM). The Artificial Compressibility Method (ACM) is (link-wise) formulated by a finite set of discrete directions (links) on a regular Cartesian grid, in analogy with LBM. The main advantage is the possibility of exploiting well established technologies originally developed for LBM and classical computational fluid dynamics, with special emphasis on finite differences, at the cost of minor changes. For instance, wall boundaries not aligned with the background Cartesian mesh can be taken into account by tracing the intersections of each link with the wall (analogously to LBM technology). LW-ACM requires no high-order moments beyond hydrodynamics (often referred to as ghost moments) and no kinetic expansion. Like finite difference schemes, only standard Taylor expansion is needed for analyzing consistency. Preliminary efforts towards optimal implementations have shown that LW-ACM is capable of similar computational speed as optimized (BGK-) LBM. In addition, the memory demand is significantly smaller than (BGK-) LBM. Two- and three-dimensional benchmarks are investigated, and an extensive comparative study between solutions obtained through FVM. Numerical evidences suggest that LW-ACM represents an excellent alternative in terms of simplicity, stability and accuracy

Sensing the real world

Title: The process of using the resources of the National School Feeding Program and purchasing products from family agriculture in the light of the experience of a Federal Institute of Education, Science and Technology. Objective of the study: The National School Feeding Program (PNAE) is a federal government program aimed at the development, learning, academic performance of students and the formation of healthy habits through food and nutritional education actions. Law 11.947/ 2009 establishes that at least 30% of the financial resource passed on by the FNDE to the institutions of the federal education network, should be directed towards the acquisition of products from family agriculture. However, many federal institutions do not use the resource for lack of information about legal procedures and how to put them into practice. In this sense, the question that poses as problem of this research is: how the campuses of the Federal Institution of Education researched can make use of the resources of the PNAE and acquire products of the familiar agriculture? The aim of this work is to propose a management process for the use of PNAE resources and acquisition of products from family agriculture in Federal Education Institutions. Procedures / Method for solving the problem: It is a descriptive research, with qualitative approach and applied nature. The troubleshooting procedures were divided into two parts: i) diagnosis of the problem: bibliographic and documentary research, semi-structured interviews with those responsible for the PNAE's campuses, with the extension director of the IF Sudeste MG rectory and with support organizations for family farmers, along with participative observation of researcher; ii) elaboration of the solution proposal: a case study was used with an institution that is considered a reference in the positive execution of the PNAE and in the purchase of Family Farming products; triangulation of the case study with the reality of IF Sudeste MG; presentation of an improved process of using FNDE resources with PNAE and procurement of family farming products for all IF Sudeste MG campuses from identified improvement points; proposal validation. This last activity took place in two moments: i) an appointment was made to an agroecology professor from IF Sudeste MG participating in the CECAF (Special Purchasing Commission for Family Farming); ii) a meeting with the extension director of the IF Sudeste MG rectory. Results: Through interviews with managers and support organizations for family farmers, it was concluded that there are some points of improvement, mentioned by them, that can be included in the IF Sudeste MG process in the use of PNAE resources. Another result obtained was the identification of improvement proposals from the process mapping already used. Thus, together with the bibliographic research, the interviews with the managers, the case study, coupled with the participant observation of the researcher, it was possible to refine the process and build a manual of procedures in the acquisition of family farming products for school feeding. Practical implications: It is suggested for IF Sudeste MG campus managers, who currently return the resource for the PNAE and / or who do not use 30% in family farming, to use the constructed artifact (procedures manual), and the proposed action plan so that they can execute this resource properly. Originality and contributions: The artifact was developed by mapping the process, understanding the legislation, reviewing other published works, and consolidating the interviews, allied to the participant observation of the researcher, since she works directly with CECAF in her work campus. The product contributes to the executing entity (EEx): i) comply with the legislation and do not run the risk of sanctioning the control agencies, ii) offer your students healthy and proper nutrition, iii) support the sustainable development of the regions around IF Sudeste MG campuses through family farming. These contributions are in line with the scientific / technological line of action - LACT 3: Competitiveness, Innovation and Entrepreneurship, as this is an internal management work, since the research is aimed at proposing an improvement in the process of using FNDE resources for PNAE and the acquisition of family farming products. Technical / Technological Production: Thus, the artifact presented here refers to a procedure manual, accompanied by an action plan. Thus, it fits as a non-patentable technical / technological product, belonging to Axis 1- Products and Processes. The procedures manual developed has potential applicability, with the proposal to be disclosed and applied in IF Sudeste MG and other institutions that are interested in using it. It is a medium production of innovation and low complexity, involving the combination of current legislation, consultation with other artifacts used by other institutions, and interviews with actors, as a reference for the development of this product.

<p>J Spec Educ Rehab 2009; 10(1-2):63-71.</p>

In this thesis a method is developed for calculating supersonic wings with curved subsonic leading edges. The linearized theory is used throughout the thesis. The wing with the curved subsonic leading edges is transformed into a wing with straight subsonic leading edges by means of a transformation as used by Coene for quasi-homogeneous approximations to the solution of this problem. The Mach cone is invariant under the transformation. The solution of the transformed Prandtl-Glauert equation is expressed in terms of Fenain's solutions for the delta wing. In general the solution is an infinite sum of terms, each term related to a solution for the delta wing. However, a condition is formulated under which certain families of wings with curved leading edges possess solutions in closed form. It is shown that any boundary value problem for such wings can be solved by the superposition of these exact solutions of the Prandtl-Glauert equation. The problem is thus reduced to determining the number of terms necessary to approximate the given boundary values within satisfactory bounds, and within a satisfactory region of the wing. One family of wings with curved leading edges that has a solution in closed form is found. The flat plate with these leading edges is studied in detail. In order to find a reasonable approximation to the flat plate, in a satisfactory region of the wing, up to five solutions are superposed. It has been found that the curvature has a considerable effect on the perturbation velocity and the leading edge suction force. The leading edge suction force thus found is compared with that calculated by some other approximate methods.

The Meshless Local Petrov-Galerkin (MLPG) method is used to analyze transient deforma- tions near either a crack or a notch tip in a linear elastic plate. The local weak formulation of equations govern- ing elastodynamic deformations is derived. It results in a system of coupled ordinary differential equations which are integrated with respect to time by a Newmark family of methods. Essential boundary conditions are imposed by the penalty method. The accuracy of the MLPG so- lution is established by comparing computed results for one-dimensional wave propagation in a rod with the an- alytical solution of the problem. Results are then com- puted for the following two problems: a rectangular plate with a central crack with plate edges parallel to the crack axis loaded in tension, and a double edge-notched plate with the edge between the notches loaded by compres- sive tractions. Stresses at points near the crack/notch tip computed from the MLPG solution are found to agree well with those obtained from either the analytical or the finite element solution of the same problem. The index of stress singularity is ascertained from a plot of log (stress) vs. log ( r) where r is the distance from the crack tip. It is found that, for the double-edge notched plate, the mode-mixity of deformations near a notch-tip in an or- thotropic plate can be adjusted by suitably varying the in-plane moduli of the material of the plate. The varia- tion of shear stress with r exhibits a boundary layer effect near r= O. tegrals appearing in the local weak formulation of the problem. Atluri et al. (1999) have pointed out that the Galerkin approximation can also be adopted that leads to a symmetric stiffness matrix. Atluri and Zhu (2000) solved elastostatic problems by the MLPG method, and Lin and Atluri (2000) introduced the upwinding scheme to analyze steady convection-diffusion problems. Ching and Batra (200 1) enriched the polynomial basis functions with those appropriate to describe singular deformation fields near a crack tip and used the diffraction criterion to find stress intensity factors, the J-integrals and sin- gular stress fields near a crack tip. Gu and Liu (2001) used the Newmark family of methods to study forced vi- brations of a beam. The problem of bending of a thin plate has been studied by Long and Atluri (2002). War- lock et al. (2002) have analyzed elastostatic deforma- tions of a material compressed in a rough rectangular cavity analytically by the Laplace transformation tech- nique and numerically by the MLPG method. Atluri and Shen (2002a,b) have demonstrated the use of different weight functions and have compared their performance with that of the Galerkin finite element method. By choosing a Heaviside step function as the test function, they eliminated the domain integration in the local weak form. Thus only boundary integrals over local subdo- mains remained in the local weak form. For elastostatic problems, this was shown to be more efficient than both the finite element and the boundary element methods. The paper is organized as follows. Section 2 gives the MLPG formulation including the local weak form, the moving least squares approximation, the discrete gov- erning equations and the time integration scheme. Cal- culations of the dynamic stress intensity factors from the near-tip stress fields are also described. Numerical ex- amples are presented in Section 3. The MLPG results are compared with either analytical or finite element so- lutions. Section 4 summarizes the conclusions.

The island of Cuba has the greatest diversity of birds in the Caribbean, and at the same time, a large number of endangered species. Illegal trade is one of major threats in Neotropical islands, because birds are captured for domestic and international illegal market. This study was undertaken with the aim to characterize the domestic market, in which captive wild birds are used as pets in the central region of Cuba. For this, a census and random survey to identify, and describe wild bird richness and abundance in 10 localities of urban and rural environments, was undertaken from August to November 2014, and from June to October 2015. Our results detected that at least 24 species and 973 individuals from six orders and 11 families were captive. The best represented order was Passeriformes (13 species), followed by Accipitriformes (four species). The best-represented families were Thraupidae (3.3 ± 0.33) and Cardinalidae (2.6 ± 0.45). Besides, the localities of Patria (17), Moron (13) and Bolivia (13) in the urban area had the highest richness. The richness of residents (5.80 ± 0.68) was higher than the endemics (1.70 ± 0.30) and migrants (2.70 ± 0.52), while the richness of endemics (2.5 ± 0.29) and residents (7.75 ± 0.63) was higher in urban areas. There were more captive species with Least Concern category (6.20 ± 1.02), but the Endangered category predominated in rural areas (12.5 %). The most common species were Passerina cyanea , Melopyrrha nigra , Tiaris olivaceus and Passerina ciris. A total of 46% of the species were classified with a tendency to decrease, 33.3 % to increase and 20.8 % to stability. The abundance of species with a tendency to decrease (63.4 ± 22.13) was higher than those that tend to stability (14.8 ± 9.9). The actual traffic will lead to species extinction, mainly parrots and raptors, threatening several ecological services. Illegal trade should be addressed as an environmental, economic and social problem. Strategy for controlling this unsustainable trade was proposed.

A theory of existence and uniqueness of bounded solutions of linear and nonlinear boundary value problems over a semi-infinite interval is developed. A numerical method for solving such problems is proposed. The method uses only finite intervals and convergence is proven as the length of the interval goes to infinity. This work is extended to problems over 0 <= t < [infinity] with a regular singular point at t = 0. The techniques developed are applied to solve three problems. i) The beam equation representing a semi-infinite pile imbedded in soil. Such problems are of interest in structural and foundation engineering. ii) An eigenvalue problem representing the solution of the Schrodinger equation for an ion of the hydrogen-molecule with fixed nuclei. iii) The Navier-Stokes equations for the von Karman swirling flow. For this problem the existence of multiple solutions has recently been discovered. We discover an additional branch of solutions and reproduce the previous results in a much simpler and more efficient manner. Our results clearly suggest that an infinite family of branches of solutions exist for this problem.

Collection of Solved Nonlinear Problems for Remote Shaping and Patterning of Liquid Structures on Flat and Curved Substrates by Electric and Thermal Fields

Very recently, Plubtieng and Kumam [S. Plubtieng, P. Kumam, Weak convergence theorem for monotone mappings and a countable family of nonexpansive mappings, J. Comput. Appl. Math. 224 (2009) 614-621] proposed an iterative algorithm for finding a common solution of a variational inequality problem for an inverse-strongly monotone mapping and a fixed point problem of a countable family of nonexpansive mappings, and obtained a weak convergence theorem. In this paper, based on Plubtieng-Kumam's iterative algorithm we introduce a new iterative algorithm for finding a common solution of a generalized mixed equilibrium problem with perturbation and a fixed point problem of a countable family of nonexpansive mappings in a Hilbert space. We first derive a strong convergence theorem for this new algorithm under appropriate assumptions and then consider a special case of this new algorithm. Moreover, we establish a weak convergence theorem for this special case under some weaker assumptions. Such a weak convergence theorem unifies, improves and extends Plubtieng-Kumam's weak convergence theorem. It is worth pointing out that the proof method of strong convergence theorem is very different from the one of weak convergence theorem.

We design the first online algorithm with poly-logarithmic competitive ratio for the edge-weighted degree-bounded Steiner forest (EW-DB-SF) problem and its generalized variant. We obtain our result by demonstrating a new generic approach for solving mixed packing/covering integer programs in the online paradigm. In EW-DB-SF, we are given an edge-weighted graph with a degree bound for every vertex. Given a root vertex in advance, we receive a sequence of terminal vertices in an online manner. Upon the arrival of a terminal, we need to augment our solution subgraph to connect the new terminal to the root. The goal is to minimize the total weight of the solution while respecting the degree bounds on the vertices. In the offline setting, edge-weighted degree-bounded Steiner tree (EW-DB-ST) and its many variations have been extensively studied since early eighties. Unfortunately, the recent advancements in the online network design problems are inherently difficult to adapt for degree-bounded problems. In particular, it is not known whether the fractional solution obtained by standard primal-dual techniques for mixed packing/covering LPs can be rounded online. In contrast, in this paper we obtain our result by using structural properties of the optimal solution, and reducing the EW-DB-SF problem to an exponential-size mixed packing/covering integer program in which every variable appears only once in covering constraints. We then design a generic integral algorithm for solving this restricted family of IPs. As mentioned above, we demonstrate a new technique for solving mixed packing/covering integer programs. Define the covering frequency k of a program as the maximum number of covering constraints in which a variable can participate. Let m denote the number of packing constraints. We design an online deterministic integral algorithm with competitive ratio of O(k*log(m)) for the mixed packing/covering integer programs. We prove the tightness of our result by providing a matching lower bound for any randomized algorithm. We note that our solution solely depends on m and k. Indeed, there can be exponentially many variables. Furthermore, our algorithm directly provides an integral solution, even if the integrality gap of the program is unbounded. We believe this technique can be used as an interesting alternative for the standard primal-dual techniques in solving online problems.