we investigate buchbaum and eisenbud's construction of the second symmetric power $s_r(x)$ of a chain complex $x$ of modules over a commutative ring $r$. we state and prove a number of results from the folklore of the subject for which we know of no good direct references. we also provide several explicit computations and examples. we use this construction to prove the following ...

Let U be an open subset of a locally compact metric ANR X and let f : U → X be a continuous map. In this paper we study the fixed point index of the map that f induces in the n-symmetric product of X, Fn(X). This index can detect the existence of periodic orbits of period ≤ n of f , and it can be used to obtain the Euler characteristic of the n-symmetric product of a manifold X, χ(Fn(X)). We co...

In 1923, Eisenhart 1 gave the condition for the existence of a second-order parallel symmetric tensor in a Riemannian manifold. In 1925, Levy 2 proved that a second-order parallel symmetric nonsingular tensor in a real-space form is always proportional to the Riemannian metric. As an improvement of the result of Levy, Sharma 3 proved that any second-order parallel tensor not necessarily symmetr...

In order to further enhance the Ni/Ce 0.8Gd0.2O2-δ (Ni/GDC20) cermet anodic performance for low temperature solid oxide fuel cell (LT-SOFC), a study was conducted on the nanostructuring of NiO/GDC composite by only once wet-infiltration of rhodium chloride precursor. By using electrochemical impedance spectroscopy (EIS) analysis, the effect of only one drop of Rh-infiltrating solution on ...

The feeding kinematics of dwarf and pygmy sperm whales (Kogia sima and K. breviceps) and bottlenose dolphins Tursiops truncatus were characterized and compared incorporating the Ram-Suction Index (RSI). Mean RSI data support a suction feeding strategy for Kogia (-0.67+/-0.29; mean +/- s.d.) and a ram feeding strategy for Tursiops (0.94+/-0.11; mean +/- s.d.). Tursiops displayed two ram-based fe...

We introduce a new VEP paradigm the Jitter Spatial Frequency (JSF) Sweep VEP that permits efficient mapping of the spatiotemporal tuning of the developmental motion asymmetry (DMA). Vertical sinewave gratings undergoing 90o horizontal oscillatory displacements (6 or 10 Hz) were presented while their SF was swept over 2 to 5 octaves during each VEP trial. JSF sweep VEPs were recorded from 28 inf...

Sea fog significantly threatens the safety of maritime activities. This paper develops a sea dataset (SFDD) and dual branch detection network (DB-SFNet). We investigate all observed events in Yellow Bohai (118.1{\deg}E-128.1{\deg}E, 29.5{\deg}N-43.8{\deg}N) from 2010 to 2020, collect images for each event Geostationary Ocean Color Imager (GOCI) comprise SFDD. The location image SFDD is accurate...

We use an optical centrifuge to align asymmetric top SO_{2} molecules by adiabatically spinning their most polarizable O-O axis. The effective centrifugal potential in the rotating frame confines the sulfur atoms to the plane of the laser-induced rotation, leading to the planar molecular alignment that persists after the molecules are released from the centrifuge. The periodic appearance of the...

Asymmetric cell divisions occur widely during many developmental processes in plants. In most angiosperms, the first zygotic cell division is asymmetric resulting in two daughter cells of unequal size and with distinct fates. However, the critical molecular mechanisms regulating this division remain unknown. Previously we showed that treatment of tobacco zygotes with beta-glucosyl Yariv (βGlcY)...