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Given a graph $F$, the planar Tur\'an number of $F$, denoted $\text{ex}_{\mathcal{P}}(n, F)$, is the maximum number of edges in an $n$-vertex $F$-free planar graph. Such an extremal graph problem was initiated by Dowden while determining…

We investigate the underlying distribution of orbital eccentricities for planets around early-to-mid M dwarf host stars. We employ a sample of 163 planets around early- to mid-M dwarfs across 101 systems detected by NASA's Kepler Mission.…

We report the discovery of forty erupting cataclysmic variable stars in the OGLE-III Galactic disk fields: seventeen objects of U Gem type, four of Z Cam type, and nineteen stars showing outbursts and superoutbursts typical for SU UMa type…

Let $X$ be a fixed projective scheme which is flat over a base scheme $S$. The association taking a quasi-projective $S$-scheme $Y$ to the scheme parametrizing $S$-morphisms from $X$ to $Y$ is functorial. We prove that this functor…

In recent years we have witnessed an explosion of photometric time-series data, collected for the purpose of finding a small number of rare sources, such as transiting extrasolar planets and gravitational microlenses. Once combed, these…

We describe the C_{2k+1}-free graphs on n vertices with maximum number of edges. The extremal graphs are unique except for n = 3k-1, 3k, 4k-2, or 4k-1. The value of ex(n,C_{2k+1}) can be read out from the works of Bondy, Woodall, and…

As part of a larger program aimed at better quantifying the uncertainties in stellar computations, we attempt to calibrate the extent of convective overshooting in low to intermediate mass stars by means of eclipsing binary systems. We…

Searching for transits provides a very promising technique for finding close-in extra-solar planets. Transiting planets present the advantage of allowing one to determine physical properties such as mass and radius unambiguously. The…

The colours of the galaxy class known as Extremely Red Objects (EROs; R-K>5) are considered to be consistent with two distinct galaxy populations at high redshift: evolved ellipticals or young dusty starbursts. In this paper the properties…

We report photometry results of a frequently outbursting dwarf nova, ER Ursae Majoris. To measure the outburst parameters of the system, we carried out analyses of the light curve, periodograms, and O-C diagrams. We investigated the…

We analyze $n - \bar n$ oscillations in generic models with large extra dimensions in which standard-model fields propagate and fermion wavefunctions have strong localization. We find that in these models $n - \bar n$ oscillations might…

Fix a field $F$. In this paper, we study the sets $\D_F(n) \subset [0,n]$ defined by [\D_F(n):= {0 \leq m \leq n: T^n-1\text{has a divisor of degree $m$ in} F[T]}.] When $\D_F(n)$ consists of all integers $m$ with $0 \leq m \leq n$, so that…

We present a long-term programme for timing the eclipses of white dwarfs in close binaries to measure apparent and/or real variations in their orbital periods. Our programme includes 67 close binaries, both detached and semi-detached and…

We prove an inequality between the conductor and the discriminant for all hyperelliptic curves defined over discretely valued fields $K$ with perfect residue field of characteristic not 2. Specifically, if such a curve is given by $y^2 =…

Given a smooth affine curve X over a field k of positive characteristic, and an overconvergent F-isocrystal on X, we prove after replacing k by a finite purely inseparable extension, there exists a finite separable cover of X, the pullback…

We present the results of UBV imaging of a large sample of irregular galaxies: 94 Im systems, 24 Blue Compact Dwarfs (BCDs), and 18 Sm galaxies. We also include JHK imaging of 41 of these galaxies. The sample spans a large range in galactic…

We produce and analyze eclipse time variation (ETV) curves for some 2600 Kepler binaries. We find good to excellent evidence for a third body in 222 systems via either the light-travel-time (LTTE) or dynamical effect delays. Approximately…

We present an updated catalog of 4680 northern eclipsing binaries (EBs) with Algol-type light curve morphology (i.e., with well-defined beginning and end of primary and secondary eclipses), using data from the Catalina Sky Surveys. Our work…

In Butler, J.Differential Geom. 39 (1):1--34,1994, the author gives a sufficient condition for a line bundle associated with a divisor D to be normally generated on $X=P(E)$ where E is a vector bundle over a smooth curve C. A line bundle…

Combining visual and spectroscopic orbits of binary stars leads to a determination of the full 3D orbit, individual masses, and distance to the system. We present a full analysis of the evolved binary system $\delta$ Delphini using…