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The duration of effective bee pollination period was limited by caging flowering branches for shorter or longer time in blooming fruit trees in a number of experiments during the past decades. In the case of self-sterile fruit species and cultivars (apples, pears, quinces, some plums, some sour cherries) even partial limitation of the effective duration of bee pollination period significantly reduced the fruit set and the yield. In the case of self-fertile apricots the effect of the total and also the influence of partial limitation of bee pollination period was the same as in the case of the mentioned self-sterile fruits. On the other hand, in the case of another self-fertile fruits (some plums, some sour cherries), the effect of partial limitation of bee pollination period was usually small, but complete (or incomplete but strong) limitation of be pollination usually resulted in a strong reduction of yield. This means that not only self-sterile but also self-fertile fruits clearly depend on insect (bee) pollination. This is because pollen dehiscence of anthers and the receptive period of stigmas do not overlap in time within the individual flowers. Stigmas in self-fertile trees, therefore, need pollen carried by bees from another flowers of the same tree (or compatible pollen from another trees). Accordingly, additional bee pollination (moving bee colonies to the orchards in flower) is needed to all kinds of temperate-zone fruit tree species when bee visitation of plantations is not abundant enough for some reasons.

This paper contains two main results. The first is an explicit construction of bipartite graphs which do not contain certain complete bipartite subgraphs and have maximal density, up to a constant factor, under this constraint. This construction represents the first significant progress in three decades on this old problem in extremal graph theory. The construction beats the previously known probabilistic lower bound on density. The proof uses the elements of commutative algebra and algebraic geometry (theory of ideals, integral extensions, valuation rings). The second result concerns monotone span programs. We obtain the first superpolynomial lower bounds for explicit functions in this model. The best previous lower bound was $\Omega(n^{5/2})$ by Beimel, Gal, Paterson (FOCS’95); our analysis exploits a general combinatorial lower bound criterion from that paper. We give two proofs of superpolynomial lower bounds; one based on an analysis of Paley-type bipartitie graphs via Weil’s character sum estimates. A third result demonstrates the power of monotone span programs by exhibiting a function computable in this model in linear size while requiring superpolynomial size monotone circuits and exponential size monotone formulae.

We put the final piece into a puzzle first introduced by Bollobas, Erdos and Szemeredi in 1975. For arbitrary positive integers $n$ and $r$ we determine the largest integer $\Delta=\Delta (r,n)$, for which any $r$-partite graph with partite sets of size $n$ and of maximum degree less than $\Delta$ has an independent transversal. This value was known for all even $r$. Here we determine the value for odd $r$ and find that $\Delta(r,n)=\Delta(r-1,n)$. Informally this means that the addition of an oddth partite set does not make it any harder to guarantee an independent transversal.In the proof we establish structural theorems which could be of independent interest. They work for all $r\geq 7$, and specify the structure of slightly sub-optimal graphs for even $r\geq 8$.

JumbleG is a Maker–Breaker game. Maker and Breaker take turns in choosing edges from the complete graph $K_n$. Maker's aim is to choose what we call an $\epsilon$-regular graph (that is, the minimum degree is at least $(\frac12-\epsilon) n$ and, for every pair of disjoint subsets $S,T\subset V$ of cardinalities at least $\epsilon n$, the number of edges $e(S,T)$ between $S$ and $T$ satisfies $\bigl|\frac{e(S,T)}{|S|\,|T|}-\frac12\bigr|\leq \epsilon$.) In this paper we show that Maker can create an $\epsilon$-regular graph, for $\epsilon\geq 2(\log n/n)^{1/3}$. We also consider a similar game, JumbleG2, where Maker's aim is to create a graph with minimum degree at least $\bigl(\frac12-\epsilon\bigr)n$ and maximum co-degree at most $\bigl(\frac14+\epsilon\bigr)n$, and show that Maker has a winning strategy for $\epsilon> 3 (\log n/n)^{1/2}$. Thus, in both games Maker can create a pseudo-random graph of density $\frac12$. This guarantees Maker's win in several other positional games, also discussed here.

The effect of the basic group of specific substrates of trypsin on the kinetics of the enzyme was studied. The basic group was substituted by methylamine added to a non-specific substrate. The kinetic constants of tryptic hydrolysis of N-acetyl-l-alanine ethyl ester involving methylamine, at pH 6.3–8.5 were determined. For comparison, the constants of trypsin and α-chymotrypsin were also determined. It can be concluded that methylamine increases the rate of hydrolysis catalyzed by trypsin. The relative increase of the pH-independent limiting value of (kc/Km)max is shown to be fivefold and the pKa decreases by 0.4 unit. The increase of kc is nearly fourfold. The rate constants of the hydrolysis steps catalyzed by trypsin and trypsin · methylamine, respectively, were assayed by means of the nucleophile 1,4-butanediol at pH 6.6. There is a sixfold increase of the original rates caused by methylamine for acylation (k2) and a threefold increase for deacylation (k3) but the substrate dissociation constant (Ks) was almost unchanged. A comparison of the individual rates of the methylamine-activated tryptic hydrolysis of nonspecific substrates with the appropriate data of the trypsin-catalyzed hydrolysis of specific substrates indicates that there is an approximately 1000-fold difference between the rate constants for the acylation step, while in deacylation the difference is insignificant. The methylammonium ion bound to trypsin is supposed to keep the enzyme through the catalysis in a more active conformation than the original one. This indirect effect might bear only a small part of the trypsin-substrate interaction.

Answering a question of Alon et al., we show that there exists an absolute constant C such that every graph G with maximum degree 5 has a vertex partition into 2 parts, such that the subgraph induced by each part has no component of size greater than C. We obtain similar results for partitioning graphs of given maximum degree into k parts (k>2) as well. A related theorem is also proved about transversals inducing only small components in graphs of a given maximum degree.

We describe several variants of the norm-graphs introduced by Kollár, Rónyai, and Szabó and study some of their extremal properties. Using these variants we construct, for infinitely many values of n, a graph on n vertices with more than 12n5/3 edges, containing no copy of K3, 3, thus slightly improving an old construction of Brown. We also prove that the maximum number of vertices in a complete graph whose edges can be colored by k colors with no monochromatic copy of K3, 3 is (1+o(1))k3. This answers a question of Chung and Graham. In addition we prove that for every fixed t, there is a family of subsets of an n element set whose so-called dual shatter function is O(mt) and whose discrepancy is Ω(n1/2−1/2tlogn). This settles a problem of Matoušek.

Let A and B be hypergraphs with a common vertex set V. In a (p,q,A∪B) Bart–Moe game, the players take turns selecting previously unclaimed vertices of V. The game ends when every vertex has been claimed by one of the players. The first player, called Bart (to denote his role as Breaker and Avoider together), selects p vertices per move and the second player, called Moe (to denote his role as Maker or Enforcer), selects q vertices per move. Bart wins the game iff he has at least one vertex in every hyperedge B∈B and no complete hyperedge A∈A. We prove a sufficient condition for Bart to win the (p,1) game, for every positive integer p. We then apply this criterion to two different games in which the first player’s aim is to build a pseudo-random graph of density pp+1, and to a discrepancy game.

LetNkbe the maximal integer such that there exist subsetsA1,. . . ,ANk⊆ {1, 2,⋯ ,n} for whichAi∩Ajis an arithmetic progression of length at leastkfor every 1 ≤i

An Avoider-Enforcer game is played by two players, called Avoider and Enforcer, on a hypergraph [email protected]?2^X. The players claim previously unoccupied elements of the board X in turns. Enforcer wins if Avoider claims all vertices of some element of F, otherwise Avoider wins. In a more general version of the game a bias b is introduced to level up the players' chances of winning; Avoider claims one element of the board in each of his moves, while Enforcer responds by claiming b elements. This traditional set of rules for Avoider-Enforcer games is known to have a shortcoming: it is not bias monotone. We relax the traditional rules in a rather natural way to obtain bias monotonicity. We analyze this new set of rules and compare it with the traditional ones to conclude some surprising results. In particular, we show that under the new rules the threshold bias for both the connectivity and Hamiltonicity games, played on the edge set of the complete graph K"n, is asymptotically equal to n/logn. This coincides with the asymptotic threshold bias of the same game played by two ''random'' players.

Let p and q be positive integers and let H be any hypergraph. In a (p,q,H) Avoider–Enforcer game two players, called Avoider and Enforcer, take turns selecting previously unclaimed vertices of H. Avoider selects p vertices per move and Enforcer selects q vertices per move. Avoider loses if he claims all the vertices of some hyperedge of H; otherwise Enforcer loses. We prove a sufficient condition for Avoider to win the (p,q,H) game. We then use this condition to show that Enforcer can win the (1,q) perfect matching game on K2n for every q⩽cn/logn for an appropriate constant c, and the (1,q) Hamilton cycle game on Kn for every q⩽cnloglogloglogn/lognlogloglogn for an appropriate constant c. We also determine exactly those values of q for which Enforcer can win the (1,q) connectivity game on Kn. This result is quite surprising as it substantially differs from its Maker–Breaker analog. Our method extends easily to improve a result of Lu [X. Lu, A note on biased and non-biased games, Discrete Appl. Math. 60 (1995) 285–291], regarding forcing an opponent to pack many pairwise edge disjoint spanning trees in his graph.

Cardiac cachexia is a co-morbidity that may develop in terminal stages of chronic heart failure (CHF). Up to 15% of ambulatory patients with heart failure are affected. Over the last decades, cardiac cachexia and alterations in muscle metabolism in heart disease have received increasing research interest. This article highlights some recent studies of cardiac cachexia that were presented at the annual meeting of the European Society of Cardiology in September 2010 in Stockholm, Sweden. Studies presented here were focused on effects of exercise training and protein degradation, particularly into the role of the ubiquitin-proteasome complex and its ubiquitin ligases MuRF-1 and MAFbx. Exercise training in patients with CHF was found to increase maximal oxygen consumption and to reduce MuRF-1 expression. Lysosomal muscle degradation does not seem to play a major role in patients with CHF, however, inflammatory cytokines such as tumor necrosis factor-a trigger muscle protein degradation. Other studies found that the serum levels of the adipokine adiponectin are elevated in patients with CHF and that these levels may be correlated with muscle mass, muscle strength in the arms, or with trunk fat mass. Another study showed that the expression of myostatin in skeletal muscle, a negative regulator of muscle growth that is essential for normal regulation of muscle mass, is decreased in spontaneously hypertensive rats with heart failure compared with control animals. This is also true for follistatin, a powerful antagonist, and its potential as a biomarker of muscle wasting. These findings may pave the way for effective treatment approaches to cardiac cachexia.

A graph G is called ( K 3 , K 3 )-co-critical if the edges of G can be coloured with two colours without getting a monochromatic triangle, but adding any new edge to the graph, this kind of ‘good’ colouring is impossible. In this short note we construct ( K 3 , K 3 )-co-critical graphs of maximal degree O(n 3 4 ) .

Vizing conjectured that @c(G@?H)>=@c(G)@c(H) for every pair G,H of graphs, where ''@?'' is the Cartesian product, and @c(G) is the domination number of the graph G. Denote by @c^i(G) the maximum, over all independent sets I in G, of the minimal number of vertices needed to dominate I. We prove that @c(G@?H)>=@c^i(G)@c(H). Since for chordal graphs @c^i=@c, this proves Vizing's conjecture when G is chordal.

The graph (non-)planarity game is played on the complete graph $K_n$ between an Enforcer and an Avoider, each of whom take one edge per round. The game ends when the edges chosen by Avoider form a non-planar subgraph. We show that Avoider can play for $3n-26$ turns, improving the previous bound of $3n-28\sqrt n$.

In a (1 : q) Maker-Breaker game, one of the central questions is to find (or at least estimate) the maximal value of q that allows Maker to win the game. Based on the ideas of Bednarska and Łuczak [Bednarska, M., and T. Łuczak, Biased positional games for which random strategies are nearly optimal, Combinatorica, 20 (2000), 477–488], who studied biased H-games, we prove general winning criteria for Maker and Breaker and a hypergraph generalization of their result. Furthermore, we study the biased version of a strong generalization of the van der Waerden games introduced by Beck [Beck, J., Van der Waerden and Ramsey type games, Combinatorica, 1 (1981), 103–116] and apply our criteria to determine the threshold bias of these games up to constant factor. As in the result of [Bednarska, M., and T. Łuczak, Biased positional games for which random strategies are nearly optimal, Combinatorica, 20 (2000), 477–488], the random strategy for Maker is again the best known strategy.

The lack of information is often cause of the insufficiency of attributes being developed and appears on the new commodity characterising its utility. Neither own nor other information is presented. For improving this handicap, we endeavoured to praise apple products grown by biological methods and explain their properties as taste, skin, colour, consistency, and size. In addition, we explore the relation between general impression and the individual properties. The scrutiny starts with collecting of primary data on 9 samples taken from biologically grown apple varieties kept over 60–90 days in a store and offered to the consumers. The test is based on an organoleptic assessment (records are registered in a questionnary). The individual judgements are processed and coefficients of correlation between the traits (taste, skin, size, colour) calculated. The validity of the mathematically proved relations is considered to be decisive judging the preferences in consumption of fruits.

A large number of studies have indicated recently that photosynthetic reaction center proteins (RC) bind successfully to nanostructures and their functional activity is largely retained. The major goal of current research is to find the most efficient systems and conditions for the photoelectric energy conversion and for the stability of this bio-nanocomposite. In our studies, we immobilized the RC protein on multiwalled carbon nanotubes (MWNT) through specific chemical binding to amine functional groups and through conducting polymer (poly(3-thiophene acetic acid), PTAA). Both structural (TEM, AFM) and functional (absorption change and conductivity) measurements has shown that RCs could be bound effectively to functionalized CNTs. The kinetics of the light induced absorption change indicated that RCs were still active in the composite and there was an interaction between the protein cofactors and the CNTs. The light generated photocurrent was measured in an electrochemical cell with transparent CNT electrode designed specially for this experiment. (C) 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim