Subloop incompatible Bol loops

We give a necessary modification of Proposition 1.18 in Nagy and Strambach (Loops in Group Theory and Lie Theory. de Gruyter Expositions in Mathematics Berlin, New York, 2002) and close the gap in the classification of differentiable Bol loops given in Figula (Manuscrp Math 121:367–385, 2006). Moreover, using the factorization of Lie groups we determine the simple differentiable proper Bol loops L having the direct product G ₁ × G ₂ of two groups with simple Lie algebras as the group topologically generated by their left translations such that the stabilizer of the identity element of L is the direct product H ₁ × H ₂ with H _i < G _i . Also if G ₁ = G ₂ = G is a simple permutation group containing a sharply transitive subgroup A, then an analogous construction yields a simple proper Bol loop. If A is cyclic and G is finite and primitive, then all such loops are classified.     

Conics in Minkowski geometries

Euclidean geometry is the only Minkowski geometry in which either there is a centrally symmetric, or a quadratic conic, or there is a conical ellipsoid or hyperboloid.     

Global hypoellipticity for first-order operators on closed smooth manifolds

The main goal of this paper is to address global hypoellipticity issues for the class of first-order pseudo-differential operators L = D_t + C(t, x,D_x), where (t, x) ∈ T × M, T is the one-dimensional torus, M is a closed manifold, and C(t, x,D_x) is a first-order pseudo-differential operator on M, smoothly depending on the periodic variable t. In the case of separation of variables, when C(t, x,D_x) = a(t)p(x,D_x) + ib(t)q(x,D_x), we give necessary and sufficient conditions for the global hypoellipticity of L. In particular, we show that the famous (P) condition of Nirenberg-Treves is neither necessary nor sufficient to guarantee the global hypoellipticity of L.     

Enhancing trading strategies with order book signals

We use high-frequency data from the Nasdaq exchange to build a measure of volume imbalance in the limit order (LO) book. We show that our measure is a good predictor of the sign of the next market order (MO), i.e., buy or sell, and also helps to predict price changes immediately after the arrival of an MO. Based on these empirical findings, we introduce and calibrate a Markov chain-modulated pure jump model of price, spread, LO and MO arrivals and volume imbalance. As an application of the model, we pose and solve a stochastic control problem for an agent who maximizes terminal wealth, subject to inventory penalties, by executing trades using LOs. We use in-sample-data (January to June 2014) to calibrate the model to 11 equities traded in the Nasdaq exchange and use out-of-sample data (July to December 2014) to test the performance of the strategy. We show that introducing our volume imbalance measure into the optimization problem considerably boosts the profits of the strategy. Profits increase because employing our imbalance measure reduces adverse selection costs and positions LOs in the book to take advantage of favourable price movements.     

Synthesis and Molecular Structure of β‐Phosphinoyl Carboxamides: An Unexpected Case of Chiral Discrimination of Hydrogen‐Bonded Dimers in the Solid State

A series of N,P,P‐trisubstituted aminophosphanes react with diphenylcyclopropenone to afford an easily separable mixture of two diastereomeric α,β‐diphenyl‐β‐phosphinoyl carboxamides in good yields. X‐ray crystal structures reveal that these compounds associate into dimers, formed from two enantiomeric units linked by two bifurcated hydrogen bonds, whereby the oxygen atom of the phosphoryl group acts as a dual acceptor for the vicinal NH and CH of a carbonyl group of a neighbouring molecule. Studies on the interconversion between diastereomeric phosphinoyl carboxamides in basic solution show that the thermodynamically most stable isomer depends on the nature of the substituent at the nitrogen atom. Simple computational calculations explain this phenomenon.     

Statistical evaluation of CZE-UV and CZE-ESI-MS data of intact α-1-acid glycoprotein isoforms for their use as potential biomarkers in bladder cancer

α-1-acid glycoprotein (AGP) is a highly heterogeneous protein that presents a vast number of isoforms (molecules of the protein differing in its peptidic and/or glycosidic moieties). In the last years, several authors have studied the potential use of AGP as a cancer biomarker. These studies focus on the correlation of different features of AGP structure (i.e. fucosylation, antennarity) with cancer or on the total protein blood concentration. In this study, the potential of CZE-UV and CZE-ESI-MS analysis of intact AGP isoforms to study the correlation of this protein with bladder cancer is shown. Samples from 16 individuals (eight healthy, eight bladder cancer) were analyzed and characterized in great detail including data on intact protein isoforms and on released glycans. The analytical data were evaluated employing different statistical techniques (ANOVA; principal component analysis, PCA; linear discriminant analysis; and partial least squares-discriminant analysis). Statistical differences between the two groups of study were observed. The best results were obtained by linear discriminant analysis of the CZE-ESI-MS data for intact AGP isoforms (93.75% of correct classification). Due to MS characterization, it can be observed that differences between the samples are mainly due to higher abundance of AGP isoforms containing tri- and tetra-antennary fucosylated oligosaccharides in cancer patients. The results show the great potential of CE-MS in combination with advanced data processing for the use of intact protein isoforms as disease biomarkers.     

On the Maximum Number of Translates in a Point Set

Given a finite set P⊆ℝ ^d , called a pattern, t _P (n) denotes the maximum number of translated copies of P determined by n points in ℝ ^d . We give the exact value of t _P (n) when P is a rational simplex, that is, the points of P are rationally affinely independent. In this case, we prove that t _P (n)=n−m _r (n), where r is the rational affine dimension of P, and m _r (n) is the r -Kruskal–Macaulay function. We note that almost all patterns in ℝ ^d are rational simplices. The function t _P (n) is also determined exactly when | P |≤3 or when P has rational affine dimension one and n is large enough. We establish the equivalence of finding t _P (n) and the maximum number s _R (n) of scaled copies of a suitable pattern R⊆ℝ⁺ determined by n positive reals. As a consequence, we show that s_Ak(n)=n-\varTheta (n^1-1/p(k))s_{A_{k}}(n)=n-\varTheta (n^{1-1/\pi(k)}) , where A _k ={1,2,…,k} is an arithmetic progression of size k, and π(k) is the number of primes less than or equal to k.     

Topological loops with three-dimensional solvable left translation group

We classify all connected topological loops having a three-dimensional solvable Lie group G as the group topologically generated by their left translations. It is surprising that to the non-nilpotent Lie group G having precisely one one-dimensional normal subgroup there are topological but no differentiable strongly left alternative loops.     

Systems of Hamilton-Jacobi equations

In this article we develop a generalization of the Hamilton-Jacobi theory, by considering in the cotangent bundle an involutive system of dynamical equations.