A characterization of Hermitian varieties as codewords

It is known that the Hermitian varieties are codewords in the code defined by the points and hyperplanes of the projective spaces $PG(r,q^2)$. In finite geometry, also quasi-Hermitian varieties are defined. These are sets of points of $PG(r,q^2)$ of the same size as a non-singular Hermitian variety of $PG(r,q^2)$, having the same intersection sizes with the hyperplanes of $PG(r,q^2)$. In the planar case, this reduces to the definition of a unital. A famous result of Blokhuis, Brouwer, and Wilbrink states that every unital in the code of the points and lines of $PG(2,q^2)$ is a Hermitian curve. We prove a similar result for the quasi-Hermitian varieties in $PG(3,q^2)$, $q=p^{h}$, as well as in $PG(r,q^2)$, $q=p$ prime, or $q=p^2$, $p$ prime, and $r\geq 4$

k-arcs and partial flocks

AbstractUsing the relationship between partial flocks of the quadratic cone K in PG(3, q), q even, and arcs in the plane PG(2, q), new results on partial flocks and short proofs for known theorems on translation generalized quadrangles of order (q2, q) and on ovoids in PG(3, q) are obtained. It is shown that large partial flocks of K containing approximately q conics, q even, are always extendable to a flock, which improves a result by Payne and Thas. Then new and short proofs are given for a theorem of Johnson on translation generalized quadrangles and a theorem of Glynn on ovoids

Small Minimal Blocking Sets inPG(2, q3)

AbstractWe extend the results of Polverino (1999, Discrete Math., 208/209, 469–476; 2000, Des. Codes Cryptogr., 20, 319–324) on small minimal blocking sets in PG(2,p3 ), p prime, p≥ 7, to small minimal blocking sets inPG (2, q3), q=ph, p prime, p≥ 7, with exponent e≥h. We characterize these blocking sets completely as being blocking sets of Rédei-type

On the size of complete caps in PG(3,2h)

AbstractLet m2′(3,q) be the largest value of k (k<q2+1) for which there exists a complete k-cap in PG(3,q), q even. In this paper, the known upper bound on m2′(3,q) is improved. We also improve a number of intervals, for k, for which there does not exist a complete k-cap in PG(3,q), q even

Cyclic arcs in PG(2, q

Abstract. B.C. Kestenband [9], J.C. Fisher, J.W.P. Hirschfeld, and J.A. Thas [3], E. Boros, and T. Szonyi [1] constructed complete (q2 -q + l)-arcs in PG(2, q2), q &gt; 3. One of the interesting properties of these arcs is the fact that they are fixed by a cyclic protective group of order q2 -q + 1. We investigate the following problem: What are the complete k-arcs in PG(2, q) which are fixed by a cyclic projective group of order k? This article shows that there are essentially three types of those arcs, one of which is the conic in PG(2, q), q odd. For the other two types, concrete examples are given which shows that these types also occur

The Classification of the Largest Caps in AG(5, 3)

AbstractWe prove that 45 is the size of the largest caps in AG(5,3), and such a 45-cap is always obtained from the 56-cap in PG(5,3) by deleting an 11-hyper-plane

A characterization of multiple (n-k)-blocking sets in projective spaces of square order

In [10], it was shown that small t-fold (n - k)-blocking sets in PG(n, q), q = p(h), p prime, h >= 1, intersect every k-dimensional space in t (mod p) points. We characterize in this article all t-fold (n k)-blocking sets in PG(n, q), q square, q >= 661, t < c(p)q(1/6)/2, vertical bar B vertical bar < tq(n-k) + 2tq(n-k-1) root q, intersecting every k-dimensional space in t (mod root q) points

Partial Ovoids and Partial Spreads of Classical Finite Polar Spaces

2000 Mathematics Subject Classification: 05B25, 51E20.We survey the main results on ovoids and spreads, large maximal partial ovoids and large maximal partial spreads, and on small maximal partial ovoids and small maximal partial spreads in classical finite polar spaces. We also discuss the main results on the spectrum problem on maximal partial ovoids and maximal partial spreads in classical finite polar spaces.The research of the fourth author was also supported by the Project Combined algorithmic and the oretical study of combinatorial structur es between the Fund for Scientific Research Flanders-Belgium (FWO-Flanders) and the Bulgarian Academy of Science

Passive Heating: Reviewing Practical Heat Acclimation Strategies for Endurance Athletes

Heat acclimation protocols—both active and passive—have been employed by athletes in an effort to attenuate the detrimental effects of heat stress on physical capacities and sports performance. Active strategies have been extensively reviewed, but have various practical and economic limitations. The purpose of this review was therefore to provide an overview of the passive strategies that have received less attention, yet may be more practical or economically viable; recommendations for athletes are also provided. With a systematic search of the relevant databases ending in June 2018, 16 articles on passive heat acclimation that met the inclusion criteria were included in the review. The review highlighted that passive heat acclimation strategies can successfully induce heat adaptations, evident by reports of improved exercise performance, thermoregulatory, cardiovascular, and perceptual responses accompanying such interventions. Based on the review it is apparent that the use of sauna, hot-water immersion and environmental chambers may be used to provide heat stress under passive conditions, for the purpose of acclimation. To maximize the thermoregulatory-adaptive responses, exercise bouts should be employed prior to passive heat stress, rather than passive heating alone, with a minimal delay between exercise and the application of heat stress. Heating bouts should have a minimum duration of 30 min per session and be employed on consecutive days, when possible, with a minimum of 6–7 exposures to induce adaptation. This review identified that information regarding the magnitude of performance changes that can occur, as well as the perceptual responses to passive heating protocols is limited. Future research should investigate the use of passive heat exposures before and/or after repeated heat training sessions, to assess if a further boost to heat adaptation can be achieved with this strategy

Intrinsic radiosensitivity of human pancreatic tumour cells and the radiosensitising potency of the nitric oxide donor sodium nitroprusside.

A panel of eight human pancreatic tumour cell lines displayed high intrinsic radioresistance, with mean inactivation doses between 2.4 and 6.5 Gy, similar to those reported for melanoma and glioblastoma. The radiosensitising potency of sodium nitroprusside, a bioreductive nitric oxide donor, was assessed in a model of metabolism-induced hypoxia in a cell micropellet. Sodium nitroprusside at 0.1 mM revealed a radiosensitising effect with an overall enhancement ratio of 1.9 compared with 2.5 for oxygen. Radiosensitising activity correlated with the enhancement of single-strand DNA breakage caused by radiation. In suspensions with cell densities of between 3% and 30% (v/v), the half-life of sodium nitroprusside decreased from 31 to 3.2 min, suggesting a value of around 1 min for micropellets. Despite this variation, the radiosensitising activity was similar in micropellets and in diluted cell suspensions. S-nitroso-L-glutathione was found to possess radiosensitising activity, consistent with a possible role of natural thiols in the storing of radiobiologically active nitric oxide adducts derived from sodium nitroprusside. As measured by a nitric oxide-specific microsensor, activation of sodium nitroprusside occurred by bioreduction, whereas S-nitroso-L-glutathione showed substantial spontaneous decomposition. Both agents appear to exert radiosensitising action through nitric oxide as its scavenging by carboxy phenyltetramethylimidazolineoxyl N-oxide (carboxy-PTI0) and oxyhaemoglobin resulted in attenuated radiosensitisation. Sodium nitroprusside was at least 10-fold more potent than etanidazole, a 2-nitroimidazole used as a reference. Our data suggest that sodium nitroprusside, a drug currently used for the treatment of hypertension, is a potential tumour radioresponse modifier