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We introduce the multivariable connected sum which is a generalization of Seki-Yamamoto's connected sum and prove the fundamental identity for these sums by series manipulation. This identity yields explicit procedures for evaluating multivariable connected sums and for giving relations among special values of multiple polylogarithms. In particular, our class of relations contains Ohno's relations for multiple polylogarithms., 27 pages, to appear in Research in the Mathematical Sciences

We establish Ohno-type identities for multiple harmonic ($q$-)sums which generalize Hoffman's identity and Bradley's identity. Our result leads to a new proof of the Ohno-type relation for $\mathcal{A}$-finite multiple zeta values recently proved by Hirose, Imatomi, Murahara and Saito. As a further application, we give certain sum formulas for $\mathcal{A}_2$- or $\mathcal{A}_3$-finite multiple zeta values., Comment: 14 pages, Some minor corrections

We show an explicit formula relating \'etale polylogarithms introduced by Wojtkowiak and finite polylogarithms introduced by Elbaz-Vincent and Gangl. This formula is an \'etale analog of Besser's formula relating Coleman's $p$-adic polylogarithms and the finite polylogarithms., Comment: 21 pages. arXiv admin note: text overlap with arXiv:1509.07653

The transition muscle between the palatopharyngeus (PP) and the superior constrictor of the pharynx (SCP) encircles the pharyngeal isthmus from behind and is designated as the palatopharyngeal sphincter (PPS). The PPS is inferred to play important roles for velopharyngeal closure, but its existence remains controversial and its roles have been regarded as being played by the SCP. The present study aimed to clarify the anatomical status and functional implications of the PPS. Macroscopic and microscopic examinations were performed on 39 and 4 cadavers, respectively. In the former, the bilateral PPSs and their adjacent structures were exposed from outside and/or inside. In the latter, the velums embedded in paraffin were cut into frontal or sagittal sections and alternately processed with HE and Azan stains. The PPS originated from the nasal aspect of the lateral half of the palatine aponeurosis and the inferior margin of the medial pterygoid plate and was distinguishable from the PP descending in and along the palatopharyngeal arch and the cranialmost portion of the SCP in its origin. It passed dorsally on the lateral side of the levator veli palatini and traversed around the salpingopharyngeal fold running longitudinally. It then entered below the SCP and ran toward the pharyngeal raphe with SCP muscle fibers intermingled. The PPS is a muscle distinct from the SCP. Its contraction produces Passavant’s ridge and conceivably enhances the efficiency of velopharyngeal closure by pressing the salpingopharyngeal fold and the musculus uvulae ridge against the velum.

We study a refinement of the symmetric multiple zeta value, called the $t$-adic symmetric multiple zeta value, by considering its finite truncation. More precisely, two kinds of regularizations (harmonic and shuffle) give two kinds of the $t$-adic symmetric multiple zeta values, thus we introduce two kinds of truncations correspondingly. Then we show that our truncations tend to the corresponding $t$-adic symmetric multiple zeta values, and satisfy the harmonic and shuffle relations, respectively. This gives a new proof of the double shuffle relations for $t$-adic symmetric multiple zeta values, first proved by Jarossay. In order to prove the shuffle relation, we develop the theory of truncated $t$-adic symmetric multiple zeta values associated with $2$-colored rooted trees. Finally, we discuss a refinement of Kaneko-Zagier's conjecture and the $t$-adic symmetric multiple zeta values of Mordell-Tornheim type., Comment: 34 pages

We give a new proof of the duality of multiple zeta values, which makes no use of the iterated integrals. The same method is also applicable to Ohno's relation for ($q$-)multiple zeta values., 5 pages, to appear in Int. J. Number Theory

Repetitive electrical microstimulation to the cortical masticatory area (CMA) evokes distinct patterns of rhythmical jaw muscle activities (RJMAs) in animals. This study aimed to investigate the characteristics of the descending projections from the CMA, associated with distinct patterns of RJMAs, to the thalamus, midbrain, pons and medulla in guinea pigs. RJMAs with continuous masseter and digastric bursts (CB-RJMAs) and stimulus-locked digastric sub-bursts (SLB-RJMAs) were induced from the anterior and posterior areas of the rostral region of the lateral agranular cortex, and chewing-like RJMAs from the rostral region of the granular cortex. Anterograde tracer, biotinylated dextran amine, was injected into the three cortical areas. The cortical area inducing CB-RJMAs had strong ipsilateral projections to the motor thalamus, red nucleus, midbrain reticular formation, superior colliculus, parabrachial nucleus, and supratrigeminal region, and contralateral projections mainly to the lateral reticular formation around the trigeminal motor nucleus (Vmo). The cortical area inducing SLB-RJMAs had moderate projections to the motor thalamus and lateral reticular formation around the Vmo, but few projections to the midbrain nuclei. The cortical area inducing chewing-like RJMAs had strong projections to the ipsilateral sensory thalamus and contralateral trigeminal sensory nuclei, and moderate projections to the lateral reticular formation. The three cortical areas consistently had few projections to the ventromedial reticular formation. The present study demonstrates that multiple direct and indirect descending projections from the CMA onto the premotor systems connecting the trigeminal motoneurons represent the neuroanatomical repertoires for generating RJMAs during the distinct phases of natural ingestive behavior.

The purpose of the present study was to classify the courses of the human sublingual artery. For this purpose, the arteries supplying the floor of the mouth and the tongue were gross anatomically investigated using 101 sides of 53 cadavers. The courses were divided into three categories: those passing medial or lateral to the hyoglossus (categories M and L) and that piercing the mylohyoid (category P); they were subdivided into five types. Category M had one type, regarded as the usual one, in which the lingual artery took the usual pattern of distribution. Categories L and P, in which the sublingual artery arose from the facial or submental artery, had the respective two types and were collectively regarded as the unusual type. Sixty-one and 36 of the 101 sides were of the usual and unusual types, respectively, the latter of which included 17 of category L and 19 of category P. The remaining four were variations of the lingual artery itself. On examining the types by gender, the usual type was more often found in females (75.6 %), whereas the unusual type was more often found in males (48.1 %). Bilateral occurrence of the same type was often found in both the usual type (77.4 %) and the unusual type (65.0 %). Existence of the sublingual artery branch significantly increased the thicknesses of the submental arteries. The classification proposed here will conceivably contribute to safer dental implant surgery and more accurate interpretation of angiographic images of arteries in the floor of the mouth.

For a non-negative integer $$n$$ , let $$E_n$$ be the $$n$$ th Euler number. In this note, for any positive integer $$n$$ , we prove the following congruences: $$\begin{aligned} {\left\{ \begin{array}{ll} E_{4n} \equiv 380n-375 \pmod {10^3}, \\ E_{4n+2} \equiv -460n+399 \pmod {10^3}. \end{array}\right. } \end{aligned}$$ Our proof is based on induction on $$n$$ and elementary direct calculations.

In this short note, we give two proofs of the infinitude of primes via valuation theory and give a new proof of the divergence of the sum of prime reciprocals by Roth's theorem and Euler-Legendre's theorem for arithmetic progressions.

In our ongoing series of anatomical studies to determine the three-dimensional architecture of the human velar muscles, we have previously reported on the palatopharyngeus. The present study deals with the musculus uvulae (MU), in which the positional relationships of its origin to the posterior nasal spine and the palatine aponeurosis, as well as the interrelation between its anatomical status and functions, have yet to be clarified. Macroscopic and microscopic examinations were performed on 25 and 2 cadavers, respectively. In the former, bilateral MUs and their adjacent structures were exposed mainly from the nasal aspect. In the latter, the soft palates embedded in paraffin were cut into frontal and sagittal sections and alternately processed with HE and Azan stains. The left and right MUs adjacent to each other were found to run longitudinally along the midline beneath the nasal aspect of velum. It was overlaid by glandular tissue that increased in amount as it coursed distally. After originating from the oral surface of palatine aponeurosis, it ran backward to cross above the sling formed by the levator veli palatini muscles of both sides and reached the tip of uvula with its muscle fibers intermingled with glandular tissue. Past studies have proposed three functions of MU to enhance the efficiency of velopharyngeal closure: space occupier, stiffness modifier, and velar extensor. All of the above-described anatomical characteristics of MU could be explained as being adapted for these functions. This implies that MU is actively responsible for maintaining the velopharyngeal closure efficiency. Clin. Anat. 27:1009–1015, 2014. © 2014 Wiley Periodicals, Inc.

Far infrared ray (FIR) energy radiated by the natural ceramics (Rhyolite) cooled FIR ceramics activates water molecules and blood circulation to stimulate skin and other tissues. The aim of our study is to make clear whether the FIR ceramics radiating FIR energy affect or not on the new bone formation in vivo and in vitro. Methods: MC3T3-E1 cells were cultured in FIR CO2 incubator. The cell proliferation and the gene expression were analyzed by using WST-8 assay kit, RT-PCR and micro array analysis. The enzyme activities were analyzed by using the apiRZYM kit. Furthermore, titanium and natural FIR ceramics compounds were implanted under the periosteium of rat skull bone by injection method. Four weeks later, the samples were examined by the light microscope and micro CT analyses. Results: Proliferation of MC3T3-E1 cell was and DNA concentrations were inhibited by FIR energy radiation. The ALP activities were accelerated and the area of calcification nodules increased on 4 weeks. The RT-PCR data showed that the gene Runx2, Osterix, BSP, OCN, Col1a1 and OPN expression of MC3T3-E1 osteoblast like cells was activated. Bone mineral density (BMD mg/cm²) of implanted sites of T50-F50, T25-F75 and F100 groups was significantly enhanced after 4 weeks compared with control groups. This data shows FIR energy radiation by the natural FIR ceramics promoted bone-forming activity of osteoblasts. Significance: This study suggested that new bioactive ceramics such us natural FIR ceramics was useful for some clinically applications to repair bone defects for example of dental implant surgery.

Little is known about projections from the cerebral cortex to the trigeminal mesencephalic nucleus (Vmes) which contains the cell bodies of primary sensory afferents innervating masticatory muscle spindles and periodontal ligaments of the teeth. To address this issue, we employed retrograde (Fluorogold, FG) and anterograde (biotinylated dextranamine, BDA) tracing techniques in the rat. After injections of FG into the Vmes, a large number of neurons were retrogradely labeled in the prefrontal cortex including the medial agranular cortex, anterior cingulate cortex, prelimbic cortex, infralimbic cortex, deep peduncular cortex and insular cortex; the labeling was bilateral, but with an ipsilateral predominance to the injection site. Almost no FG-labeled neurons were found in the somatic sensorimotor cortex. After BDA injections into the prefrontal cortex, anterogradely labeled axon fibers and boutons were distributed bilaterally in a topographic pattern within the Vmes, but with an ipsilateral predominance to the injection site. The rostral Vmes received more preferential projections from the medial agranular cortex, while the deep peduncular cortex and insular cortex projected more preferentially to the caudal Vmes. Several BDA-labeled axonal boutons made close associations (possible synaptic contacts) with the cell bodies of Vmes neurons. The present results have revealed the direct projections from the prefrontal cortex to the primary sensory neurons in the Vmes and their unique features, suggesting that deep sensory inputs conveyed by the Vmes neurons from masticatory muscle spindles and periodontal ligaments are regulated with specific biological significance in terms of the descending control by the cerebral cortex.

To clarify features of direct projections from the primary somatosensory cortex (S1) to premotoneurons for the jaw-closing (JC) and jaw-opening (JO) components of the trigeminal motor nucleus, biotinylated dextranamine (BDA) and Fluorogold (FG) were used as the anterograde and retrograde tracers. The BDA and FG injections were made in the S1 and the JC or JO component, respectively, in rats. The distribution of FG-labeled JC and JO premotoneurons receiving contact(s) from BDA-labeled axon terminals of S1 neurons was quantitatively examined; the contacts were identified microscopically by using a X100 oil immersion objective. The largest and second largest numbers of JC and JO premotoneurons with contact(s) were found in the lateral reticular formation at the levels of the caudal pons and the medulla oblongata (cpmLRt) and trigeminal oral nucleus (Vo) bilaterally, and they comprised about 80% of the total premotoneurons with contact(s). The percentage of premotoneurons with contact(s) was higher in the Vo than in the cpmLRt for both JC and JO premotoneurons. Most of the JC or JO premotoneurons found in the nucleus of the solitary tract, inter- and supratrigeminal regions, mesencephalic trigeminal nucleus, parabrachial nucleus and reticular formation medial to the JO component of the trigeminal motor nucleus hardly received contact(s) from S1 neurons. This suggests that the contribution of S1 to the control of jaw movements is mediated via JC and JO premotoneurons located primarily in the cpmLRt and Vo areas of the brainstem.

We prove the $\boldsymbol{p}$-adic duality theorem for the finite star-multiple polylogarithms. That is a generalization of Hoffman's duality theorem for the finite multiple zeta-star values., Comment: 11 pages

In order to clarify differences in the digestion and absorption process of raw and heated defatted soybean meals (SBM) in juvenile yellowtail Seriola quinqueradiata, the fish were force-fed with the two kinds of SBMs as well as raw fish and fish meal as control, and post-feeding changes in digesta quality, serum constituent concentrations, and protein digestibility were determined. The intestinal digesta contents were higher in the fish fed with either SBM than those in the fish fed with raw fish during the experimental period. The digesta in the raw SBM-fed group passed rapidly through the stomach and intestine at a similar speed as in the raw fish-fed group, but the solubility and digestibility of the intestinal digesta protein and serum free amino acid concentration were lowest among the four protein sources, probably due to the activity of trypsin inhibitor in raw SBM. On the other hand, the digesta in the heated SBM-fed group passed slowly through the digestive tracts, and the solubility of the intestinal digesta protein was higher than that in the raw SBM group, while being similar to that in the fish meal-fed group. These results indicate that the digestion and absorption process of raw SBM was disturbed by its trypsin inhibitor, but was improved by heating to a similar degree to fish meal under the experimental conditions.

Little is known about the organization of corticofugal projections controlling antagonistic jaw muscles. To address this issue, we employed retrograde (Fluorogold; FG) and anterograde (biotinylated dextran amine; BDA) tracing techniques in rats. Three groups of premotoneurons were identified by injecting FG into the jaw-closing (JC) and -opening (JO) subdivisions of the trigeminal motor nucleus (Vmo). These were 1) the intertrigeminal region (Vint) and principal trigeminal sensory nucleus for JC nucleus; 2) the reticular region medial to JO nucleus (RmJO) for JO nucleus; and 3) the parabrachial (Pb) and supratrigeminal (Vsup) nuclei, reticular regions medial and ventral to JC nucleus, rostrodorsomedial oralis (Vor), and juxtatrigeminal region (Vjuxt) containing a mixture of premotoneurons to both the nuclei. Subsequently, FG was injected into the representative premotoneuron structures. The JC and JO premotoneurons received main afferents from the lateral and medial agranular fields of motor cortex (Agl and Agm), respectively, whereas afferents to the nuclei with both JC and JO premotoneurons arose from Agl also and from primary somatosensory cortex (S1). Finally, BDA was injected into each of the three cortical areas representing the premotoneuron structures to complement the FG data. The Agl and Agm projected to reticular regions around the Vmo, whereas the Pb, Vsup, Vor, and Vjuxt received input from Agl. The S1 projected to the trigeminal sensory nuclei as well as to the Pb, Vsup, and Vjuxt. These results suggest that corticofugal projections to Vmo via premotoneuron structures consist of multiple pathways, which influence distinct patterns of jaw movements.