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In recent years, many useful applications of the polynomial method have emerged in finite geometry. Indeed, algebraic curves, especially those defined by Rédei-type polynomials, are powerful in studying blocking sets. In this paper, we reverse the engine and study when blocking sets can arise from rational points on plane curves over finite fields. We show that irreducible curves of low degree cannot provide blocking sets and prove more refined results for cubic and quartic curves. On the other hand, using tools from number theory, we construct smooth plane curves defined over F p of degree at most 4 p 3 / 4 + 1 whose points form blocking sets. [ABSTRACT FROM AUTHOR]

Queuing network models have been extensively used for performance evaluation in many modern manufacturing and communication systems. The phenomenon of feedback reflects many practical situations, e.g. reworking in the production systems. However, existing research on open queuing network with feedback mainly concentrates on the models with infinite buffers or the models with finite buffers but exponentially distributed inter-arrival and service times. Research on open queuing networks with finite buffers, feedback and general inter-arrival and service times has not been reported. In this paper, a Rate Iterative Method embedded with the Generalised Expansion Method, is proposed for modelling this type of queuing network. System performance measures include the mean throughput, work-in-process and sojourn time all calculated by the proposed method. The accuracy and the efficiency of the proposed method are tested by comparing the results with other methods or simulation results from the experiments. Finally, a case study of a practical production system used in the manufacturing industry is studied and illustrates the applications of the proposed method. The results in this paper can be used as a basis for system design analysis and resource planning. [ABSTRACT FROM PUBLISHER]

A full classification (up to equivalence) of all minimal blocking sets in Desarguesian projective planes of order ≤8 was obtained by computer. The resulting numbers of minimal blocking sets are tabulated according to size of the set and order of the automorphism group. For the minimal blocking sets with the larger automorphism groups explicit descriptions are given. Some of these results can also be generalised to Desarguesian projective planes of higher order. [ABSTRACT FROM AUTHOR]

Minimal linear codes are algebraic objects which gained interest in the last 20 years, due to their link with Massey's secret sharing schemes. In this context, Ashikhmin and Barg provided a useful and a quite easy-to-handle sufficient condition for a linear code to be minimal, which has been applied in the construction of many minimal linear codes. In this paper, we generalize some recent constructions of minimal linear codes which are not based on Ashikhmin–Barg's condition. More combinatorial and geometric methods are involved in our proofs. In particular, we present a family of codes arising from particular blocking sets, which are well-studied combinatorial objects. In this context, we will need to define cutting blocking sets and to prove some of their relations with other notions in blocking sets' theory. At the end of the paper, we provide one explicit family of cutting blocking sets and related minimal linear codes, showing that infinitely many of its members do not satisfy the Ashikhmin–Barg's condition. [ABSTRACT FROM AUTHOR]

Bruen, see [5], and Bruen and Thas, see [7], proved that in P G (2 , q 2) a blocking set of type (1 , q + 1) 1 is either a Baer subplane or a unital. In this paper a cone-generalization of this result in P G (3 , q 2) is provided. [ABSTRACT FROM AUTHOR]

A strong triangle blocking arrangement is a geometric arrangement of some line segments in a triangle with certain intersection properties. It turns out that they are closely related to blocking sets. We prove a classification theorem for strong triangle blocking arrangements. As an application, we obtain a new proof of the result of Ackerman, Buchin, Knauer, Pinchasi and Rote which says that n points in general position cannot be blocked by n - 1 points, unless n = 2, 4. We also conjecture an extremal variant of the blocking points problem. [ABSTRACT FROM AUTHOR]

A famous conjecture of Ryser states that every r-partite hypergraph has vertex cover number at most r 1 times the matching number. In recent years, hypergraphs meeting this conjectured bound, known as r-Ryser hypergraphs, have been studied extensively. It was proved by Haxell, Narins, and Szabo that all 3-Ryser hypergraphs with matching number nu > 1 are essentially obtained by taking nu disjoint copies of intersecting 3-Ryser hypergraphs. Abu-Khazneh showed that such a characterization is false for r = 4 by giving a computer generated example of a 4-Ryser hypergraph with nu = 2 whose vertex set cannot be partitioned into two sets such that we have an intersecting 4-Ryser hypergraph on each of these parts. Here we construct first infinite families of r-Ryser hypergraphs, for any fixed matching number nu > 1, that are truly nonintersecting in the sense that they do not contain two vertex disjoint intersecting r-Ryser subhypergraphs. [ABSTRACT FROM AUTHOR]

Ecological exploitation research generally holds that cooperation alliances form without restrictions and the information within alliances is known exactly. However, these assumptions do not always accord with reality. The main aim of this paper is to develop a more realistic approach in order to analyze alliance formation and profit allocation from ecological exploitation. We define an extended fuzzy graph cooperative game, in which players partially participating in coalitions and payoffs are fuzzy numbers, called bi-fuzzy graph cooperative game. The average tree solution (short for A-T solution) based on players' risk preferences is proposed for this cooperative game, and the existence of the solution is proved. This paper can demonstrate that the players' profitability depends not only on their marginal contribution degree to the coalition, but also on the communication structure and players' positions in coalitions of a cooperative game. [ABSTRACT FROM AUTHOR]

In an earlier paper we developed a unified approach to the extendability problem for arcs in PG(k - 1, q) and, equivalently, for linear codes over finite fields. We defined a special class of arcs called (t mod q)-arcs and proved that the extendabilty of a given arc depends on the structure of a special dual arc, which turns out to be a (t mod q)-arc. In this paper, we investigate the general structure of (t mod q)-arcs. We prove that every such arc is a sum of complements of hyperplanes. Furthermore, we characterize such arcs for small values of t, which in the case t = 2 gives us an alternative proof of the theorem by Maruta on the extendability of codes. This result is geometrically equivalent to the statement that every 2-quasidivisible arc in PG(k - 1, q), q ≥ 5, q odd, is extendable. Finally, we present an application of our approach to the extendability problem for caps in PG(3, q). [ABSTRACT FROM AUTHOR]

We show that, for small t, the smallest set that blocks the long secants of the union of t pairwise disjoint Baer subplanes in PG(2,q2) has size t(q+1) and consists of t Baer sublines, and, for large t, the smallest such set has size q2+q+1 and is itself a Baer subplane of PG(2,q2). We also present a stability result in the first case. [ABSTRACT FROM AUTHOR]

The article examines the voting power indices behavior of U.S. Financial Accounting Standards Board (FASB). The author has identified various possible coalitions of voters and calculated measures of the real voting power of these coalitions to test their descriptive ability. According to the author the voting power has two dimensions, the nominal voting power and real voting power. The author has based his analysis of the past coalitions on the voting patterns for FASB Statement Nos. 1-44. The primary coalition is defined as the public accountants' voting bloc.

Reliable operation of the feeding system plays a crucial role in ensuring the safe and efficient production of the working face of backfilling gob-side entry retaining (GER). In the process of vertical feeding of the roadside support body material, the problem of blocking of the feeding shaft has occurred to the test mine, which seriously affects the production safety in mines. In this paper, based on the theoretical analysis, a fluid-solid coupling numerical model was established. The change rules of the speed of sacked gangue, pressure of air below it, and speed vector distribution with different vent diameters were obtained. The blocking mechanism of the feeding system was revealed. The results show that if the exhaust vent of the stock bin was shut, the speed of gangue in the mine increased and then decreased and finally blocked in the feeding shaft. If the exhaust vent of the stock bin was opened for pressure discharge, with the increase of diameter of the exhaust vent, the maximum speed and ending speed of sacked gangue increased, pressure differential reduced, and speed vector was uniformly distributed. The energy criterion of blocking of the feeding shaft was further obtained. Based on the engineering conditions of the test mine, when the feeding shaft is blocked, the critical value of diameter of the exhaust vent is 30 mm. The research results provide basis for the design of key parameters of the vertical feeding system, ensuring the safe and efficient production of gob-backfilled GER working face. [ABSTRACT FROM AUTHOR]

Let H be a hyperbolic quadric in P G ( 3 , q ) , where q is a prime power. Let E (respectively, T ) denote the set of all lines of P G ( 3 , q ) which are external (respectively, tangent) to H . We characterize the minimum size blocking sets in P G ( 3 , q ) , q ≠ 2 , with respect to the line set E ∪ T . We also give an alternate proof characterizing the minimum size blocking sets in P G ( 3 , q ) with respect to the line set E for all odd q . [ABSTRACT FROM AUTHOR]

In this paper we completely characterize the words with second minimum weight in the p -ary linear code generated by the rows of the incidence matrix of points and hyperplanes of PG ( n , q ) , with q = p h and p prime, proving that they are the scalar multiples of the difference of the incidence vectors of two distinct hyperplanes of PG ( n , q ) . [ABSTRACT FROM AUTHOR]

Paul Erdős and László Lovász established by means of an example that there exists a maximal intersecting family of k -sets with ⌊ ( e − 1 ) k ! ⌋ blocks, where e is the base of natural logarithm. László Lovász conjectured that their example is best known example which has the maximum number of blocks. Later it was disproved. But the quest for such examples remain valid till this date. In this note we compute the transversal size of a certain series of intersecting families of k -sets, which is constructed over the Cyclic graph. It helps to provide an example of maximal intersecting family of k -sets with so many blocks and to present two worthwhile examples which disprove two special cases of one of the conjectures of Frankl et al. [ABSTRACT FROM AUTHOR]

The equivalence problem of F q -linear sets of rank n of PG ( 1 , q n ) is investigated, also in terms of the associated variety, projecting configurations, F q -linear blocking sets of Rédei type and MRD-codes. We call an F q -linear set L U of rank n in PG ( W , F q n ) = PG ( 1 , q n ) simple if for any n -dimensional F q -subspace V of W , L V is P Γ L ( 2 , q n ) -equivalent to L U only when U and V lie on the same orbit of Γ L ( 2 , q n ) . We prove that U = { ( x , Tr q n / q ( x ) ) : x ∈ F q n } defines a simple F q -linear set for each n . We provide examples of non-simple linear sets not of pseudoregulus type for n > 4 and we prove that all F q -linear sets of rank 4 are simple in PG ( 1 , q 4 ) . [ABSTRACT FROM AUTHOR]

We study values for transferable utility games enriched by a communication graph. The most well-known such values are component-efficient and characterized by some deletion link property. We study efficient extensions of such values: for a given component-efficient value, we look for a value that (i) satisfies efficiency, (ii) satisfies the link-deletion property underlying the original component-efficient value, and (iii) coincides with the original component-efficient value whenever the underlying graph is connected. Béal et al. (Soc Choice Welf 45:819-827, 2015) prove that the Myerson value (Myerson in Math Oper Res 2:225-229, 1977) admits a unique efficient extension, which has been introduced by van den Brink et al. (Econ Lett 117:786-789, 2012). We pursue this line of research by showing that the average tree solution (Herings et al. in Games Econ Behav 62:77-92, 2008) and the compensation solution (Béal et al. in Int J Game Theory 41:157-178, 2012b) admit similar unique efficient extensions, and that there exists no efficient extension of the position value (Meessen in Communication games, 1988; Borm et al. in SIAM J Discrete Math 5:305-320, 1992). As byproducts, we obtain new characterizations of the average tree solution and the compensation solution, and of their efficient extensions. [ABSTRACT FROM AUTHOR]

This paper presents an alternative to the Traditional Gear Design (TGD) concept as well as to some modern approaches, including the Direct Dear Design (DGD) method, which separates gear geometry definition from tool selection. The proposed method called the Combined Blocking Contours (CBC) concept represents a system of some combination of various mathematical and graphic approaches and allows defining the shift coefficients as well as many other quality characteristics of involute gearing of a single-row planetaiy mechanism named usually as 2K-h type. The CBC concept provides the optimal choice for the geometrical parameters of gearings and can be effectively used at the initial stage of a gear design for both: when designing involute planetaiy reducer and animator, thus, achieving the best quality of a mechanism as a whole. [ABSTRACT FROM AUTHOR]

One problem in cooperative game theory is to model situations when two players refuse to cooperate (or the problem of quarreling members in coalitions). One example of such exclusions is the coalition statements of parliamentary parties. Other situations in which incompatible players affect the outcome are teams in firms and markets, for example. To model these exclusions in cooperative game theory, the excluded coalitions value (jE value) was introduced. This value is based on the Shapley value and takes into account that players exclude coalitions with other players. In this article, we deduce some properties of this new value. After some general results, we analyze the apex game that could be interpreted as a team situation and the glove game that models markets where sellers and buyers deal. For team situations, we show that all employees have a common interest for cooperation. On asymmetric markets, excluding coalitions affect the market players of the scarce side to a higher extent. [ABSTRACT FROM AUTHOR]

This paper presents a novel method for first quantization matrix estimation for non-aligned double JPEG compressed images. The non-aligned double JPEG scenario poses several challenges in the form of recompression artifacts which needs to be handled effectively in order to arrive at accurate first quantization estimate. One such recompression artifact which is prominent in the non-aligned scenario is the blocking artifacts arising due to the misalignment of the DCT grids in the successive compression cycles. The proposed method investigates the impact of the blocking artifacts induced errors on the DCT histogram and counters these errors via a novel DCT histogram filtering strategy. In addition, the residual noise which is also a recompression artifact is countered utilizing the local rank transform which adaptively filters the residual noise effects. The filtered histograms are compared with a synthetically created ideal second quantization matrix to estimate the degree of similarity between the two cases. Utilizing the maximum degree of similarity, the selection of first quantization value is performed. Experimental analysis utilizing several non-aligned double compressed JPEG images taken from UCID and RAISE datasets with Quality Factor (QF) of second compression being greater than the first compression ( Q F 2 > Q F 1 ) along with the comparative analysis with one of the state-of-the-art method shows accurate estimation of the first quantization values for the proposed method. The proposed method finds its application in image forensics as well as in steganalysis. [ABSTRACT FROM AUTHOR]

If B is a minimal blocking set of size less than 3(q+1)=2 in PG(2,q), q is a power of the prime p, then Szőnyi’s result states that each line meets B in 1 (mod p) points. It follows that B cannot have bisecants, i.e., lines meeting B in exactly two points. If q >13, then there is only one known minimal blocking set of size 3(q+1)=2 in PG(2, q), the so-called projective triangle. This blocking set is of Rédei type and it has 3(q-1)=2 bisecants, which have a very strict structure. We use polynomial techniques to derive structural results on Rédei type blocking sets from information on their bisecants. We apply our results to point sets of PG(2, q) with few odd-secants.In particular, we improve the lower bound of Balister, Bollobás, Füredi and Thompson on the number of odd-secants of a (q+2)-set in PG(2, q) and we answer a related open question of Vandendriessche. We prove structural results for semiovals and derive the non existence of semiovals of size q+3 when p≠3 and q>5. This extends a result of Blokhuis who classified semiovals of size q+2, and a result of Bartoli who classified semiovals of size q+3 when q ≤ 17. In the q even case we can say more applying a result of Szőnyi and Weiner about the stability of sets of even type. We also obtain a new proof to a result of Gács and Weiner about (q+t, t)-arcs of type (0, 2, t) and to one part of a result of Ball, Blokhuis, Brouwer, Storme and Szőnyi about functions over GF(q) determining less than (q+3)/2 directions. [ABSTRACT FROM AUTHOR]

We introduce group graded basic Morita equivalences between algebras determined by blocks of normal subgroups, and by using the extended Brauer quotient, we show that they induce graded basic Morita equivalences at local levels. [ABSTRACT FROM AUTHOR]

The concept of restriction, which is an extension of that of interior operator, was introduced to model limited cooperation in cooperative game theory. In this paper, a fuzzy version of restrictions is presented. We show that these new operators, called fuzzy restrictions, can be characterized by the transitivity of the fuzzy dependence relations that they induce. As an application, we introduce cooperative games with fuzzy restriction, which are used to model cooperative situations in which each player in a coalition has a level of cooperation within the coalition. A value for these games is defined and characterized. [ABSTRACT FROM AUTHOR]

We study two-sided matching problem considered in Abizada (Theor Econ 11(2), 735-756, 2016), where one side (colleges) can make monetary transfers (offer stipends) to the other (students) subject to budget constraints. Colleges have strict preferences over sets of students and value money only to the extent that it allows them to enroll better or additional students. A student can attend at most one college and receive a stipend from it. Each student has preferences over college-stipend bundles. Although in the presence of budget constraints, the conditions that are essential for most of the results on stability in the literature fail, Abizada (Theor Econ 11(2), 735-756, 2016) shows that for this model a pairwise stable allocation always exists. In this paper, we show that starting from an arbitrary allocation, there is a sequence of allocations, each allocation being obtained from the previous one by 'satisfying' a blocking pair, such that the final allocation is pairwise stable. [ABSTRACT FROM AUTHOR]

We describe small dominating sets of the incidence graphs of finite projective planes by establishing a stability result that shows that dominating sets are strongly related to blocking and covering sets. Our main result states that if a dominating set in a projective plane of order [ABSTRACT FROM AUTHOR]

In this paper we examine the problem of linear and nonlinear secure network coding from a finite geometric point of view and give some negative and positive results if we require information theoretic security based on Cai and Yeung [N. Cai and R. W. Yeung, Secure Network Coding. Proceedings of the 2002 IEEE International Symposium on Information Theory (ISIT 2002), 2002.]. On the one hand we show that there is no universal secure network coding scheme. On the other hand we give a little improvement of the result of [N. Cai and R. W. Yeung, Secure Network Coding. Proceedings of the 2002 IEEE International Symposium on Information Theory (ISIT 2002), 2002.] for the bound of the size of the coding alphabet, and a bound similar to Feldman et al. [J. Feldman, T. Malkin, C. Stein, and R. A. Servedio, On the Capacity of Secure Network Coding. Proc. 42nd Annual Allerton Conference on Communication, Control, and Computing, 2004.]. Furthermore we present results for known linear network codings: we give some necessary and some sufficient conditions for the existence of optimal linear secure network coding, when the coding scheme is given.

The sequence in which problems of different concepts are studied during instruction impacts concept learning. For example, several problems of a given concept can be studied together (blocking) or several problems of different concepts can be studied together (interleaving). In the current study, we demonstrate that the 2 sequences impact concept induction differently as they differ in the temporal spacing and the temporal juxtaposition of to-be-learned concept problems, and in the cognitive processes they recruit. Participants studied 6 problems of 3 different statistical concepts, and then were tested on their ability to correctly classify new problems on a final test. Interleaving problems of different to-be-learned concepts, rather than blocking problems by concept, enhanced classification performance, replicating the interleaving effect (Experiment 1). Introducing temporal spacing between successive problems decreased classification performance in the interleaved schedule--consistent with the discriminative-contrast hypothesis that interleaving fosters between-concept comparisons--and increased classification performance in the blocked schedule--consistent with the study-phase retrieval hypothesis that temporal spacing causes forgetting and subsequent retrieval enhances memory (Experiment 2). Temporally juxtaposing problems of concepts 3-at-a-time rather than 1-at-a-time improved overall classification performance, particularly in a blocked schedule--consistent with the commonality-abstraction hypothesis that blocking fosters within-concept comparisons (Experiment 3). All participants also completed a working memory capacity (WMC) task, findings of which suggest that the efficacy of the above study sequences may be related to individual differences in WMC. [ABSTRACT FROM AUTHOR]

We show that every i-tight set in the Hermitian variety H(2r +1, q) is a union of pairwise disjoint (2r +1)-dimensional Baer subgeometries PG(2r +1, √q) and generators of H(2r +1, q), if q ≥ 81 is an odd square and i <(q2/3 -1)/2. We also show that an i-tight set in the symplectic polar space W(2r +1, q) is a union of pairwise disjoint generators of W(2r +1, q), pairs of disjoint r-spaces {Δ, Δ⊥}, and (2r +1)-dimensional Baer subgeometries. For W(2r +1, q) with r even, pairs of disjoint r-spaces {Δ, Δ⊥} cannot occur. The (2r +1)-dimensional Baer subgeometries in the i-tight set of W(2r +1, q) are invariant under the symplectic polarity ⊥ of W(2r +1, q) or they arise in pairs of disjoint Baer subgeometries corresponding to each other under ⊥. This improves previous results where i < q5/8/√2+1 was assumed. Generalizing known techniques and using recent results on blocking sets and minihypers, we present an alternative proof of this result and consequently improve the upper bound on i to (q2/3 -1)/2. We also apply our results on tight sets to improve a known result on maximal partial spreads in W(2r +1, q). [ABSTRACT FROM AUTHOR]

Summary The basic mechanisms underlying noxious cold perception are not well understood. We developed Drosophila assays for noxious cold responses. Larvae respond to near-freezing temperatures via a mutually exclusive set of singular behaviors–in particular, a full-body contraction (CT). Class III (CIII) multidendritic sensory neurons are specifically activated by cold and optogenetic activation of these neurons elicits CT. Blocking synaptic transmission in CIII neurons inhibits CT. Genetically, the transient receptor potential (TRP) channels Trpm, NompC, and Polycystic kidney disease 2 (Pkd2) are expressed in CIII neurons, where each is required for CT. Misexpression of Pkd2 is sufficient to confer cold responsiveness. The optogenetic activation level of multimodal CIII neurons determines behavioral output, and visualization of neuronal activity supports this conclusion. Coactivation of cold- and heat-responsive sensory neurons suggests that the cold-evoked response circuitry is dominant. Our Drosophila model will enable a sophisticated molecular genetic dissection of cold nociceptive genes and circuits. [ABSTRACT FROM AUTHOR]

A pair of points x , y in a Riemannian manifold ( M , g ) is said to be secure if there exists a finite set of points intercepting every geodesic segment joining x to y . Given any conformal equivalence class C of Riemannian metrics on a closed manifold M of dimension at least two and given any pair of points x , y in M , there exists a dense G δ set C ′ ⊂ C such that x and y are not secure for every metric g in C ′ . [ABSTRACT FROM AUTHOR]

Let E (respectively; T , S ) denote the set of all lines which are external (respectively; tangent, secant) to an irreducible conic in P G ( 2 , q ) . We give a brief survey of the known results regarding the minimum size L -blocking sets of P G ( 2 , q ) for L ∈ { E , S , T ∪ E , T ∪ S } and study the other two cases when L = T , E ∪ S . [ABSTRACT FROM AUTHOR]

In the full rectangular version of Gilbert's planar tessellation (see Gilbert (1967), Mackisack and Miles (1996), and Burridge et al. (2013)), lines extend either horizontally (with east- and west-growing rays) or vertically (north- and south-growing rays) from seed points which form a stationary Poisson point process, each ray stopping when it meets another ray that has blocked its path. In the half-Gilbert rectangular version, east- and south-growing rays, whilst having the potential to block each other, do not interact with west and north rays, and vice versa. East- and south-growing rays have a reciprocality of blocking, as do west and north. In this paper we significantly expand and simplify the half-Gilbert analytic results that we gave in Burridge et al. (2013). We also show how the idea of reciprocality of blocking between rays can be used in a much wider context, with rays not necessarily orthogonal and with seeds that produce more than two rays. [ABSTRACT FROM AUTHOR]

We introduce the notion of t-quasidivisible arc as an ( n, w)-arc in $$\hbox {PG}(k-1,q)$$ such that every hyperplane has multiplicity congruent to $$n+i$$ modulo q, where $$i\in \{0,1,\ldots ,t\}$$ . We prove that every t-quasidivisible arc associated with a Griesmer code and satisfying an additional numerical condition is t times extendable. [ABSTRACT FROM AUTHOR]

In this article, we investigate collections of 'well-spread-out' projective (and linear) subspaces. Projective k-subspaces in $$\mathsf {PG}(d,\mathbb {F})$$ are in 'higgledy-piggledy arrangement' if they meet each projective subspace of co-dimension k in a generator set of points. We prove that the higgledy-piggledy set $$\mathcal {H}$$ of k-subspaces has to contain more than $$\min \left\{ |\mathbb {F}|,\sum _{i=0}^k\left\lfloor \frac{d-k+i}{i+1}\right\rfloor \right\} $$ elements. We also prove that $$\mathcal {H}$$ has to contain more than $$(k+1)\cdot (d-k)$$ elements if the field $$\mathbb {F}$$ is algebraically closed. An r-uniform weak ( s, A) subspace design is a set of linear subspaces $$H_1,\ldots ,H_N\le \mathbb {F}^m$$ each of rank r such that each linear subspace $$W\le \mathbb {F}^m$$ of rank s meets at most A among them. This subspace design is an r-uniform strong ( s, A) subspace design if $$\sum _{i=1}^N\mathrm {rank}(H_i\cap W)\le A$$ for $$\forall W\le \mathbb {F}^m$$ of rank s. We prove that if $$m=r+s$$ then the dual ( $$\{H_1^\bot ,\dots ,H_N^\bot \}$$ ) of an r-uniform weak (strong) subspace design of parameter ( s, A) is an s-uniform weak (strong) subspace design of parameter ( r, A). We show the connection between uniform weak subspace designs and higgledy-piggledy subspaces proving that $$A\ge \min \left\{ |\mathbb {F}|,\sum _{i=0}^{r-1}\left\lfloor \frac{s+i}{i+1}\right\rfloor \right\} $$ for r-uniform weak or strong ( s, A) subspace designs in $$\mathbb {F}^{r+s}$$ . We show that the r-uniform strong $$(s,r\cdot s+\left( {\begin{array}{c}r\\ 2\end{array}}\right) )$$ subspace design constructed by Guruswami and Kopparty (based on multiplicity codes) has parameter $$A=r\cdot s$$ if we consider it as a weak subspace design. We give some similar constructions of weak and strong subspace designs (and higgledy-piggledy subspaces) and prove that the lower bound $$(k+1)\cdot (d-k)+1$$ over algebraically closed field is tight. [ABSTRACT FROM AUTHOR]

We complete the classification of transitive hyperovals with groups of order divisible by $$\textit{four}$$ . [ABSTRACT FROM AUTHOR]

A blocking semioval is a set of points in a projective plane that is both a blocking set (i.e., every line meets the set, but the set contains no line) and a semioval (i.e., there is a unique tangent line at each point). The minimum size of a blocking semioval is currently known in all projective planes of order < 11, with the exception of PG(2, 9). In this note we show by demonstration of an example that the smallest blocking semioval in PG(2, 9) has size 21 and investigate some properties of this set. [ABSTRACT FROM AUTHOR]

The modified-offered-load approximation can be used to choose a staffing function (the time-varying number of servers) to stabilize delay probabilities at target levels in multi-server delay models with time-varying arrival rates, with or without customer abandonment. In contrast, as we confirm with simulations, it is not possible to stabilize blocking probabilities to the same extent in corresponding loss models, without extra waiting space, because these probabilities necessarily change dramatically after each staffing change. Nevertheless, blocking probabilities can be stabilized provided that we either randomize the times of staffing changes or average the blocking probabilities over a suitably small time interval. We develop systematic procedures and study how to choose the averaging parameters. [ABSTRACT FROM AUTHOR]

In this paper some relations between finite geometric spaces and cooperative games are considered. In particular by some recent results on blocking sets we have new results on blocking coalitions. Finally we introduce a new research field on the possible relations between quasihypergroups and cooperative games.