Exponential Renormalization II: Bogoliubov's R-operation and momentum subtraction schemes

This article aims at advancing the recently introduced exponential method for renormalisation in perturbative quantum field theory. It is shown that this new procedure provides a meaningful recursive scheme in the context of the algebraic and group theoretical approach to renormalisation. In particular, we describe in detail a Hopf algebraic formulation of Bogoliubov's classical R-operation and counterterm recursion in the context of momentum subtraction schemes. This approach allows us to propose an algebraic classification of different subtraction schemes. Our results shed light on the peculiar algebraic role played by the degrees of Taylor jet expansions, especially the notion of minimal subtraction and oversubtractions.Comment: revised versio

Composition-Diamond lemma for λ\lambda-differential associative algebras with multiple operators

In this paper, we establish the Composition-Diamond lemma for $\lambda$-differential associative algebras over a field $K$ with multiple operators. As applications, we obtain Gr\"{o}bner-Shirshov bases of free $\lambda$-differential Rota-Baxter algebras. In particular, linear bases of free $\lambda$-differential Rota-Baxter algebras are obtained and consequently, the free $\lambda$-differential Rota-Baxter algebras are constructed by words

Infection of skipjack tuna Katsuwonus pelamis (Linnaeus 1758) of Oman Sea with cestode Trypanorhyncha (Diesing 1863)

Numerous reports on existence of white cysts in musculature of skipjack tuna Katsuwonus pelamis and lack of information about the quality of cysts and individual responses of fish to them led the authors to focus on this fish as a commercially valuable species. This study investigated the histopathologic responses of skipjack tuna to highly prevalent cystic larval stages of Trypanorhyncha. Some 92.25% of 400 examined skipjack tuna of Oman Sea (Iran) captured from processing center in Chabahar have been diagnosed infected by Trypanorhyncha Larvae through gross muscle examination. Minimum of 5 to maximum of 19 cysts were observed per each flank flesh with no significant difference between number of cysts from right (9 ± 4) and left flanks (10 ± 4) and also males and females (p>.05, t- student test (spss version 16)). Using hematoxylin and eosin (H&E) staining of 4µm sections of surrounded cysts with muscle and light microscopy observations each metacestode was distinguished encapsulated by surrounding fibrous cyst wall consists of thin inner layer and a thick outer layer with the minimal histopathologic changes around it. The highly prevalent Trypanorhyncha infection in Oman Sea represents the high rate of infection among elasmobranches. The ability of encapsulated parasite to escape from the immune system of the host is assumed as one reason for the observed minimal tissue response in infected fish and the continuation of infection among elasmobranches and teleosts of Omen Sea

Localization of gravity in brane world with arbitrary extra dimensions

We study the induced 4-dimensional linearized Einstein field equations in an m-dimensional bulk space by means of a confining potential. It is shown that in this approach the mass of graviton is quantized. The cosmological constant problem is also addressed within the context of this approach. We show that the difference between the values of the cosmological constant in particle physics and cosmology stems from our measurements in two different scales, small and large.Comment: 8 pages. arXiv admin note: substantial text overlap with arXiv:gr-qc/0408004, arXiv:gr-qc/0607067, arXiv:0704.1035, arXiv:0707.3558, arXiv:0710.266

Effects of Voluntary Resistance Exercise Training During Recovery From Hindlimb Unloading on Rat Gastrocnemius Muscle

As research continues to examine the deleterious impact of long-duration spaceflight on human muscle mass and function, there remain gaps in our knowledge of muscle physiology, especially in examining how muscle’s ability to recover or rehabilitate from unloading may alter the results of multiple exposures to microgravity followed by 1g recovery. The purpose of this study was to analyze the effects of resistance exercise training of gastrocnemius muscle mass and anabolism during the initial recovery period immediately following a bout of unloading, as well as to examine the role that exercise may have on a subsequent period of weightlessness. This was achieved in rodent models of simulated spaceflight (0g), recovery (1g), and resistance training (\u3e1g) using male Sprague-Dawley (6 mo) rats randomly assigned to the following groups: 28d hindlimb unloading (HU), 28d HU followed by a 56d recovery period of normal cage ambulation at 1g (1HU+REC), 2 cycles of 28d HU with a 56d recovery period between unloading (2HU), 2HU followed by an additional 56d recovery at 1g (2HU+REC), or an age- and housing-matched control group (CON). In addition, following the initial 28d HU period, two groups of animals were given 7d recovery at 1g followed by a 7wk (3 sessions/wk) moderate-intensity, moderate-volume voluntary resistance exercise program (EX) in which the animals were trained to perform a squat-like motion with full extension of the lower limb and resistance was applied incrementally by weighted pouches over the scapula to ~65% bodyweight. At the conclusion of the experiments, gastrocnemius muscles were carefully excised, weighed, and evaluated for cumulative (24h) rates of protein synthesis (FSR). Values of both muscle mass and FSR were lower than control during periods of unloading (p\u3c0.05), but with recovery, control values were reached for mass and surpassed for FSR. Interestingly, there was no significant difference between the mass of 2HU and 2HU+EX (p\u3e0.05), and both were diminished in comparison to control animals, suggesting that benefits of exercise during periods of ambulatory reloading after disuse/microgravity may not be additive. In conclusion, our data suggest that given adequate recovery, microgravity-induced losses of muscle mass can be fully restored to control values, and this adaptational response persists even with multiple exposures. These findings may have important implications not only for career astronauts, but also for individuals who have been subjected to casting of a limb or a period of bed rest following severe injury or illness

An algebraic scheme associated with the noncommutative KP hierarchy and some of its extensions

A well-known ansatz (`trace method') for soliton solutions turns the equations of the (noncommutative) KP hierarchy, and those of certain extensions, into families of algebraic sum identities. We develop an algebraic formalism, in particular involving a (mixable) shuffle product, to explore their structure. More precisely, we show that the equations of the noncommutative KP hierarchy and its extension (xncKP) in the case of a Moyal-deformed product, as derived in previous work, correspond to identities in this algebra. Furthermore, the Moyal product is replaced by a more general associative product. This leads to a new even more general extension of the noncommutative KP hierarchy. Relations with Rota-Baxter algebras are established.Comment: 59 pages, relative to the second version a few minor corrections, but quite a lot of amendments, to appear in J. Phys.

Quantum Corrections for a Braneworld Black Hole

By using the quantum tunneling approach over semiclassical approximations, we study the quantum corrections to the Hawking temperature, entropy and Bekenstein-Hawking entropy-area relation for a black hole lying on a brane.Comment: 8 pages, accepted for publication in IJTP, references adde

DEPTOR Expression Correlates with Muscle Protein Synthesis

Mammalian target of rapamycin (mTOR) has long been declared a focal point of muscle protein synthesis. mTORC1 (an mTOR complex consisting of mTOR, raptor, PRAS40, and mLST8) has been associated with regulation of protein translation in muscle, altering expression and activity levels of key downstream targets S6K1 and eIF-4E-BP1. mTORC1 has been shown to be affected by various stimuli, including nutritional status, growth factors, and mechanical loading. But in past incidents we have found disconnects in muscle protein synthesis and mTOR signaling, stimulating discussions that mTOR content and activation alone may not be able to fully account for muscle protein synthesis. Gaining popularity as a target for anti-cancer therapies, we became interested in DEPTOR, an endogenous inhibitor of mTORC1. Pharmacological inhibition of DEPTOR in cell culture and mouse studies has displayed increases of anabolic signaling in response to atrophic circumstances. We present two unique catabolic conditions in which we explore DEPTOR expression and muscle protein synthesis and demonstrate the first known data proposing that DEPTOR expression is not only influenced by physiological stimuli, including mechanical loading and insulin sensitivity, but that DEPTOR expression strongly correlates with 24-hr cumulative muscle protein synthesis rates. In one study, male Sprague Dawley rats were subjected to various conditions of musculoskeletal unloading, reloading, and overload, in which hindlimb unloading (HU) was utilized to mimic chronic disuse atrophy (28-d), followed by ambulatory reloading (56-d post HU) with and without the addition of resistance exercise prescribed to assist in recovery (3 sessions/wk for 7-wks; progressive increases in added resistance up to ~60% BW). DEPTOR expression was assessed via Immunoblotting. 24-hr cumulative muscle protein synthesis (FSR) was measured via stable isotope labeling and quantified by gas chromatogram/mass spectrometry. DEPTOR demonstrated a strong negative correlation with FSR in the gastrocnemius (r = - 0.93261; p \u3c0.01). In our second study, male obese Zucker rats were divided into their lean and obese phenotypes, as well as placed into sedentary and resistance exercised groups. DEPTOR and FSR were assessed as described above following operant conditioning and four progressive exercise sessions over 9-d. Gastrocnemius DEPTOR/FSR was again significant (r = - 0.75723; p\u3c0.01). Collectively, these results are the first to associate physiologic changes in DEPTOR expression with alterations of FSR, which may have important implications towards the design of therapeutic targets for the control of muscle mass or in evaluating muscle anabolism

From Rota-Baxter Algebras to Pre-Lie Algebras

Rota-Baxter algebras were introduced to solve some analytic and combinatorial problems and have appeared in many fields in mathematics and mathematical physics. Rota-Baxter algebras provide a construction of pre-Lie algebras from associative algebras. In this paper, we give all Rota-Baxter operators of weight 1 on complex associative algebras in dimension $\leq 3$ and their corresponding pre-Lie algebras.Comment: 23 pages, appear in Journal of Physics A; Mathematical and Theoretica