About Gods, I Don\u27t Believe in None of That Shit, the Facts Are Backwards: Slaughterhouse\u27s Lyrical Atheism

Hip Hop group Slaughterhouse\u27s multi-membered, perversely holy quadrinity provides a fertile site for a pseudo-non-theological theological reading-a theology with and without god, that is, with god\u27s titular presence but bereft of any ethos of a mover and shaker god. God, in my reading of Slaughterhouse\u27s lyrics, is impotent. Rather than the Word, Slaughterhouse publishes sacred texts (albums and mixtapes) that speak to Black embodied life; their albums are the scriptural holy ghetto-Word, the Gospels that of Royce, Crooked, Joell, and Joey, rather than Matthew, Mark, Luke, and John. Through the lyrics of Slaughterhouse\u27s songs, they craft a god that is but is not; a god that does lyrical work in the sense that the name of god has cultural capital and produces effects, but is not God, that is, a being that commands the heavens and the Earth

Extremal Colorings and Independent Sets

We consider several extremal problems of maximizing the number of colorings and independent sets in some graph families with fixed chromatic number and order. First, we address the problem of maximizing the number of colorings in the family of connected graphs with chromatic number k and order n where k≥4 role= presentation style= box-sizing: inherit; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3ek≥4k≥4. It was conjectured that extremal graphs are those which have clique number k and size (k2)+n−k role= presentation style= box-sizing: inherit; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3e(k2)+n−k(k2)+n−k. We affirm this conjecture for 4-chromatic claw-free graphs and for all k-chromatic line graphs with k≥4 role= presentation style= box-sizing: inherit; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3ek≥4k≥4. We also reduce this extremal problem to a finite family of graphs when restricted to claw-free graphs. Secondly, we determine the maximum number of independent sets of each size in the family of n-vertex k-chromatic graphs (respectively connected n-vertex k-chromatic graphs and n-vertex k-chromatic graphs with c components). We show that the unique extremal graph is Kk∪En−k role= presentation style= box-sizing: inherit; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eKk∪En−kKk∪En−k, K1∨(Kk−1∪En−k) role= presentation style= box-sizing: inherit; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eK1∨(Kk−1∪En−k)K1∨(Kk−1∪En−k) and (K1∨(Kk−1∪En−k−c+1))∪Ec−1 role= presentation style= box-sizing: inherit; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3e(K1∨(Kk−1∪En−k−c+1))∪Ec−1(K1∨(Kk−1∪En−k−c+1))∪Ec−1 respectively

Zero Energy Bound States in Many--Particle Systems

It is proved that the eigenvalues in the N--particle system are absorbed at zero energy threshold, if none of the subsystems has a bound state with $E \leq 0$ and none of the particle pairs has a zero energy resonance. The pair potentials are allowed to take both signs

Toward Reliable Modeling of S-nitrosothiol Chemistry: Structure and Properties of Methyl Thionitrite (CH3SNO), an S-nitrosocysteine Model

Methyl thionitrite CH3SNO is an important model of S-nitrosated cysteine aminoacid residue (CysNO), a ubiquitous biological S-nitrosothiol (RSNO) involved in numerous physiological processes. As such, CH3SNO can provide insights into the intrinsic properties of the —SNO group in CysNO, in particular, its weak and labile S—N bond. Here, we report an ab initio computational investigation of the structure and properties of CH3SNO using a composite Feller-Peterson-Dixon scheme based on the explicitly correlated coupled cluster with single, double, and perturbative triple excitations calculations extrapolated to the complete basis set limit, CCSD(T)-F12/CBS, with a number of additive corrections for the effects of quadruple excitations, core-valence correlation, scalar-relativistic and spin-orbit effects, as well as harmonic zero-point vibrational energy with an anharmonicity correction. These calculations suggest that the S—N bond in CH3SNO is significantly elongated (1.814 Å) and has low stretching frequency and dissociation energy values, νS—N = 387 cm−1 and D0 = 32.4 kcal/mol. At the same time, the S—N bond has a sizable rotation barrier, △ role= presentation style= display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 20px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px 2px 0px 0px; margin: 0px; position: relative; \u3e△△E0≠ role= presentation style= display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 12px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px 2px 0px 0px; margin: 0px; position: relative; \u3e≠≠ = 12.7 kcal/mol, so CH3SNO exists as a cis- or trans-conformer, the latter slightly higher in energy, △ role= presentation style= display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 20px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px 2px 0px 0px; margin: 0px; position: relative; \u3e△△E0 = 1.2 kcal/mol. The S—N bond properties are consistent with the antagonistic nature of CH3SNO, whose resonance representation requires two chemically opposite (antagonistic) resonance structures, CH3—S+=N—O−and CH3—S−/NO+, which can be probed using external electric fields and quantified using the natural resonance theory approach (NRT). The calculated S—N bond properties slowly converge with the level of correlation treatment, with the recently developed distinguished cluster with single and double excitations approximation (DCSD-F12) performing significantly better than the coupled cluster with single and double excitations (CCSD-F12), although still inferior to the CCSD(T)-F12 method that includes perturbative triple excitations. Double-hybrid density functional theory (DFT) calculations with mPW2PLYPD/def2-TZVPPD reproduce well the geometry, vibrational frequencies, and the S—N bond rotational barrier in CH3SNO, while hybrid DFT calculations with PBE0/def2-TZVPPD give a better S—N bond dissociation energy

Gravitational Collapse of Circularly Symmetric Stiff Fluid with Self-Similarity in 2+1 Gravity

Linear perturbations of homothetic self-similar stiff fluid solutions, $S[n]$, with circular symmetry in 2+1 gravity are studied. It is found that, except for those with $n = 1$ and $n = 3$, none of them is stable and all have more than one unstable mode. Hence, {\em none of these solutions can be critical}.Comment: latex file, 1 figure; last version to appear in Prog. Theor. Phy

Finiteness of irreducible holomorphic eta quotients of a given level

We show that for any positive integer N, there are only finitely many holomorphic eta quotients of level N, none of which is a product of two holomorphic eta quotients other than 1 and itself. This result is an analog of Zagier’s conjecture/Mersmann’s theorem which states that of any given weight, there are only finitely many irreducible holomorphic eta quotients, none of which is an integral rescaling of another eta quotient. We construct such eta quotients for all cubefree levels. In particular, our construction demonstrates the existence of irreducible holomorphic eta quotients of arbitrarily large weights

Effect of large- and small- bodied zooplankton on phytoplankton in a eutrophic oxbow

Macrozooplankton and microzooplankton effects on the phytoplankton were measured in situ in a eutrophic lake. Indigenous phytoplankton were incubated for 5 days in 301 mesocosms with either the macro- and microzooplankton (complete), microzooplankton only (micro) or no zooplankton (none). Changes in phytoplankton biovolume were investigated. Rotifer densities became significantly higher in the 'micro' treatment than in the 'complete' and 'none' treatments. Total algal biovolume changed little in the 'complete' and 'none' treatments, but increased significantly in the 'micro' treatment. The results suggest that macrozooplankton (Daphnia magna) suppressed it and microzooplankton (Keratella cochlearis) enhanced it. They had opposite net effects on the phytoplankton. Suppression of microzooplankton by Daphnia probably had an indirect negative effect on the phytoplankton

Double node neighborhoods and families of simply connected 4-manifolds with b^+=1

We introduce a new technique that is used to show that the complex projective plane blown up at 6, 7, or 8 points has infinitely many distinct smooth structures. None of these smooth structures admit smoothly embedded spheres with self-intersection -1, i.e. they are minimal. In addition, none these smooth structures admit an underlying symplectic structure. Shortly after the appearance of a preliminary version of this article, Park, Stipsicz, and Szabo used the techniques described herein to show that the complex projective plane blown up at 5 points has infinitely many distinct smooth structures. In the final section of this paper we give a somewhat different construction of such a family of examples.Comment: 11 pages, More typos and minor errors correcte