Primitive Elements Research Articles

Geology and petrology of the potassic and ultrapotassic rocks from the northern part of Senirkent (Isparta-SW Turkey): evidence of magma–carbonate wall-rock interactions

Potassic, ultrapotassic lava domes, flows, and volcano-sedimentary deposits including leucite-bearing and leucite-free grains crop out to the north of Senirkent (Isparta), at the apex of the Isparta Angle (southwestern Turkey). Ultrapotassic rocks are nepheline-foidolite, italite, leucitite, melilite leucitite, melilite-gehlenite leucitite, diopside leucitite, and leucitophyre with lowest SiO2 content (38.71–44.72 wt%, but the leucitophyre has 51.4 wt%), higher K2O (4.36–10.19 wt%), MgO (3.25–6.98 wt%), and K2O/Na2O ratio (2.65–32.8). Potassic rocks are phonolitic leucitites, sanidine-phyric phonolite, and trachytes with SiO2 (49.35–64.46 wt%), K2O (8.28–11.38 wt%), MgO (0.17–1.39 wt%), and K2O/Na2O ratio (2.25–11.8). Some leucitites, diopside leucitites, and phonolitic leucitites enclose partly carbonatite occurences or associated with carbonate-rich part including carbonatite globules, phlogopite, clinopyroxene, and/or leucite, melanite crystals embedded in glassy volcanic matrix and/or carbonate matrix. Primitive mantle-normalized incompatible element patterns display strong enrichments in LILEs (Cs, Rb, Ba, U, Th, Sr) relative to HFSEs (Nb, Ti) with distinct negative Nb–Ti anomalies, suggesting subduction-related lavas. Chondrite-normalized REE patterns are characterized by light REE enrichment (251–493 times chondrite for La) and flat heavy REE patterns (10–27 times chondrite for Yb). All the leucite-bearing and leucite-free rocks display similar, subparallel chondrite-normalized and primitive mantle-normalized trace element patterns, suggesting cogenetic origin. Mineralogical, petrological, and geochemical data suggest magma–carbonate wall-rock interaction and tapping of different parts of the melts within the magma chamber along the fault lines formed during neotectonic period and extension-related block faulting.

An early Devonian intra-plate bimodal volcanic suite in the Kyrgyz North Tianshan belt, the central Asian orogenic belt

A suite of bimodal volcanic rocks in the Kyrgyz North Tianshan belt is composed of totally ∼100-m-thick basalt and basaltic andesite layers of the Karakastek Formation and totally ∼700-m-thick rhyolite layers of the Kastek Formation, with minor amounts of interlayered felsic to intermediate tuff/ignimbrite. Zircon grains from a rhyolite sample have a weighted mean 206Pb/238U age of 416 ± 8 Ma, which is considered to be the crystallization age of the rhyolite. The zircon grains have δ18O ranging from +6.5 to +7.3‰. The calculated zircon saturation temperatures (TZr) range from 850 to 900 °C. Rhyolites have high total alkaline, Zr, Y and Nb contents and high Ga/Al similar to A1-type granitoids formed in an intra-plate setting. Mafic volcanic rocks have SiO2 ranging from 49.4 to 55.3 wt% and FeOt/MgO from 1.4 to 2.4, showing a tholeiitic trend. They have negative Nb and Ta anomalies on the primitive mantle-normalized trace element patterns and have εNd(t) of −1.5 to 0. There is a positive correlation between εNd(t) and ΔεHf(t) of the mafic volcanic rocks, indicative of crustal contamination. However, one least evolved basalt sample has Mg# of 57 with low Zr and Hf concentrations, indicating insignificant crustal contamination. Modeling results indicate that the mafic volcanic rocks may have been derived from a dry, garnet-bearing lherzolite mantle source. They have εHf(t) and εNd(t) varying along the “Island arc array”, which is interpreted as the mantle source was metasomatized by slab-derived melts rather than fluids. In addition, the rhyolites have εNd(t) of −2.4 to −2.9, much lower than the mafic volcanic rocks, and were thus unlikely produced by the fractionation of basaltic magmas. The rhyolites show Nd-Hf isotope decoupling, which is interpreted as a result of the anataxis of Precambrian lower crust associated with the breakdown of garnet. Therefore, the early Devonian bimodal volcanic suite in the Kyrgyz North Tianshan belt was considered to have formed in an intra-plate setting.

Bi-interpretability of some monoids with the arithmetic and applications

We will prove bi-interpretability of the arithmetic $${\mathbb {N}}= \langle N, +,\cdot , 0, 1\rangle $$ and the weak second order theory of $${\mathbb {N}}$$ with the free monoid $$\mathbb {M}_X$$ of finite rank greater than 1 and with a non-trivial partially commutative monoid with trivial center. This bi-interpretability implies that finitely generated submonoids of these monoids are definable. Moreover, any recursively enumerable language in the alphabet X is definable in $$\mathbb {M}_X$$ . Primitive elements, and, therefore, free bases are definable in the free monoid. It has the so-called QFA property, namely there is a sentence $$\phi $$ such that every finitely generated monoid satisfying $$\phi $$ is isomorphic to $$\mathbb {M}_X$$ . The same is true for a partially commutative monoid without center. We also prove that there is no quantifier elimination in the theory of any structure that is bi-interpretable with $$\mathbb {N}$$ to any boolean combination of formulas from $$\Pi _n$$ or $$\Sigma _n$$ .

Translation Equivalence of Boolean Functions Expressed by Primitive Element

Translation Equivalence of Boolean Functions Expressed by Primitive Element

Accelerated tower arithmetic

Nowadays, asymptotically fast algorithms are widely used in computer algebra for computations in towers of algebraic field extensions of small height. Yet it is still unknown how to reach softly linear time for products and inversions in towers of arbitrary height. In this paper we design the first algorithm for general ground fields with a complexity exponent that can be made arbitrarily close to one from the asymptotic point of view. We deduce new faster algorithms for changes of tower representations, including the computation of primitive element representations in subquadratic time.

Somatic mutations in early metazoan genes disrupt regulatory links between unicellular and multicellular genes in cancer.

Extensive transcriptional alterations are observed in cancer, many of which activate core biological processes established in unicellular organisms or suppress differentiation pathways formed in metazoans. Through rigorous, integrative analysis of genomics data from a range of solid tumors, we show many transcriptional changes in tumors are tied to mutations disrupting regulatory interactions between unicellular and multicellular genes within human gene regulatory networks (GRNs). Recurrent point mutations were enriched in regulator genes linking unicellular and multicellular subnetworks, while copy-number alterations affected downstream target genes in distinctly unicellular and multicellular regions of the GRN. Our results depict drivers of tumourigenesis as genes that created key regulatory links during the evolution of early multicellular life, whose dysfunction creates widespread dysregulation of primitive elements of the GRN. Several genes we identified as important in this process were associated with drug response, demonstrating the potential clinical value of our approach.

Stable haptic feedback generation for mid-air gesture interactions: a hidden Markov model-based motion synthesis approach

Generation of stable and realistic haptic feedback during mid-air gesture interactions have recently garnered significant research interest. However, the limitations of the sensing technologies such as unstable tracking, range limitations, nonuniform sampling duration, self occlusions, and motion recognition faults significantly distort motion based haptic feedback to a large extent. In this paper, we propose and implement a hidden Markov model (HMM)-based motion synthesis method to generate stable concurrent and terminal vibrotactile feedback. The system tracks human gestures during interaction and recreates smooth, synchronized motion data from detected HMM states. Four gestures—tapping, three-fingered zooming, vertical dragging, and horizontal dragging—were used in the study to evaluate the performance of the motion synthesis methodology. The reference motion curves and corresponding primitive motion elements to be synthesized for each gesture were obtained from multiple subjects at different interaction speeds by using a stable motion tracking sensor. Both objective and subjective evaluations were conducted to evaluate the performance of the motion synthesis model in controlling both concurrent and terminal vibrotactile feedback. Objective evaluation shows that synthesized motion data had a high correlation for shape and end-timings with the reference motion data compared to measured and moving average filtered data. The mean R^{2} values for synthesized motion data was always greater than 0.7 even under unstable tracking conditions. The experimental results of subjective evaluation from nine subjects showed significant improvement in perceived synchronization of vibrotactile feedback based on synthesized motion.

Petrology and geochemistry of Upper Jurassic Weimei Formation sandstones in southern Tibet: implications for provenance and tectonic setting

Located within the centre of the Tethys Himalayas, the Weimei Formation of the Rongbu area in southern Tibet is a littoral- neritic sedimentary association composed of clastic rocks and a few shales. Petrologic characteristics and detrital component statistics indicate that sandstone types include lithic quartz sandstones, with the average content of quartz, feldspar and debris being 77%, 9% and 14%, respectively. The provenance of the Weimei Formation is a recycled orogeny, and the aforementioned sandstones generally have high SiO2 levels, low CaO, K2O and Na2O levels and wide ranges of CIA and CIW values. The primitive mantle-normalised trace element spider diagrams showed unstable content of some elements and losses of Ba, P, Sr, K, Ti and other elements in partial samples. Chondrite-normalised rare-earth element (REE) patterns indicate that the sandstones are characterised by an enrichment of LREE, significant fractionation of LREE and HREE and negative Eu anomalies. Further, ratios of Sm/Nd and Cr/Zr and discriminant diagrams (i.e., La/Yb versus ΣREE, ΣREE versus SiO2/Al2O3, La/Th versus Hf and function discrimination diagrams) reveal that sandstones from the Weimei Formation were derived from ancient quartzose sedimentary rocks and volcanic rocks of continental island arc. Many important parameters (i.e., La, Ce, Pb, Th, Hf, Zr, ΣREE, La/Yb, (La/Yb)N, ΣLREE/ΣHREE, Eu/Eu*, Rb/Sr and Zr/Hf) of samples and tectonic setting discriminant diagrams (i.e., Th versus Co versus Zr/10, La versus Th versus Sc, La versus Th and function discriminant diagrams) indicate that the tectonic setting of the Weimei Formation sandstones from the Tethys Himalayas has both characteristics of a passive margin and continental island arc. By comparing the detrital zircon U-Pb ages and Hf isotopic characteristics of the Weimei Formation with the strata whose provenances have been identified and analysing the weathering, petrography and geochemistry characteristics of Weimei Formation sandstones and the paleogeography conditions of the northern margin of the India craton within the Late Jurassic epoch, we inferred that Weimei Formation sandstones were mainly sourced from the Precambrian metamorphic rocks of the India craton, simultaneously, the sandstones also received minor sedimentary materials from earlier Tethys Himalaya strata whose provenances contained volcanic rocks of the nearby Gangdese volcanic belt. After experiencing weak to moderate weathering, denudation and long-distance transport, the sedimentary materials eventually migrated to the shelf and the top of the continental slope on the northern margin of the Indian continent, where the materials later participated in diagenesis.

Development of Complex Energy Systems with Absorption Technology by Combining Elementary Processes

Optimal design of energy systems ultimately aims to develop a methodology to realize an energy system that utilizes available resources to generate maximum product with minimum components. For this aim, several researches attempt to decide the optimal system configuration as a problem of decomposing each energy system into primitive process elements. Then, they search the optimal combination sequentially from the minimum number of constituent elements. This paper proposes a bottom-up procedure to define and explore configurations by combining elementary processes for energy systems with absorption technology, which is widely applied as a heat driven technology and important for improving system’s energy efficiency and utilizing alternative energy resources. Two examples of application are presented to show the capability of the proposed methodology to find basic configurations that can generate the maximum product. The demonstration shows that the existing absorption systems, which would be calculated based on the experience of designers, could be derived by performing optimization with the synthesis methodology automatically under the simplified/idealized operating conditions. The proposed bottom-up methodology is significant for realizing an optimized absorption system. With this methodology, engineers will be able to predict all possible configurations and identify a simple yet feasible optimal system configuration.

Primitive and Almost Primitive Elements of Schreier Varieties

A variety of linear algebras is said to be Schreier if any subalgebra of a free algebra of this variety is free. A system of elements of a free algebra is primitive if there is a complement of this system with respect to a free generating set of the free algebra. An element of a free algebra of a Schreier variety is said to be almost primitive if it is not primitive in the free algebra, but it is a primitive element of any subalgebra that contains it. This survey article is devoted to the study of primitive and almost primitive elements of Schreier varieties.

Pair of primitive elements with prescribed traces over finite fields

In this article, we establish a sufficient condition for the existence of a primitive element such that for any matrix of rank 2, the element is a primitive element of and , for any prescribed , where for some positive integer k. We establish existence of such elements for all pairs except for finitely many pairs.

Little and big q-Jacobi polynomials and the Askey–Wilson algebra

The little and big q-Jacobi polynomials are shown to arise as basis vectors for representations of the Askey–Wilson algebra. The operators that these polynomials respectively diagonalize are identified within the Askey–Wilson algebra generated by twisted primitive elements of $$\mathfrak U_q(sl(2))$$. The little q-Jacobi operator and a tridiagonalization of it are shown to realize the equitable embedding of the Askey–Wilson algebra into $$\mathfrak U_q(sl(2))$$.

U-Pb geochronology, bulk-rock geochemistry and petrology of Late Cretaceous syenitic plutons in the Gölköy (Ordu) area (NE Turkey): Implications for magma generation in a continental arc extension triggered by slab roll-back

Late Cretaceous felsic plutons in the Eastern Pontides orogenic belt of Turkey are found in varying ages, sizes and compositions. The Late Cretaceous syenitic bodies, namely Direkli and Yeniköy Tepe plutons in the Ordu area, intruded into the Late Cretaceous volcanics and volcanoclastics, and compositionally consist of syenite and minor quartz-syenite with mainly granular and rarely porphyric, poikilitic and perthitic textures. The studied plutons contain K-feldspar, plagioclase, quartz, clinopyroxene, biotite and minor hornblende, and Fe-Ti oxide, apatite, and zircon. Mineral thermobarometer estimations imply that the syenitic plutons were crystallized in P-T conditions representing mid to shallow crustal levels. Petrochemically, these syenitic plutons show I-type, metaluminous-peraluminous transitional (A/CNK = 0.85–1.04) and shoshonitic features. LA-ICP-MS U-Pb zircon dating on the syenitic plutons yielded weighted mean ages of 78.5–72 Ma. Primitive mantle-normalized trace element patterns of the studied plutons are characterized by negative anomalies of Ba, Sr, Nb, Ta and Ti, and enrichment in Rb, Th, K, Ce and La. The chondrite-normalized rare earth element (REE) plots of the studied plutons show moderately enriched concave-shaped patterns (LaN/LuN = 10.3–10.7 for the Direkli pluton; LaN/LuN = 6.8–11.7 for the Yeniköy Tepe pluton) with negative Eu anomalies. The plutons have 87Sr/86Sr ratios (0.705368–0.706954), 143Nd/144Nd ratios (0.512600–0.512672), 206Pb/204Pb ratios (19.29–19.52) and 207Pb/204Pb ratios (15.65–15.67). The geochemical data, as well as regional geology, suggest that the Late Cretaceous syenitic plutons have formed in an extensional continental arc setting triggered by slab roll-back. The parental magma of syenitic plutons was derived from melts of lower crustal materials (metabasalt/metaandesite) and lithospheric mantle component.

GK dimension of some connected Hopf algebras

While it was identified that the growth of any connected Hopf algebras is either a positive integer or infinite, we have yet to determine the Gelfand–Kirillov (GK) dimension of a given connected Hopf algebra. We use the notion of anti-cocommutative elements introduced in Wang, D. G., Zhang, J. J., Zhuang, G. (2013). Coassociative lie algebras. Glasgow Math. J. 55(A):195–215 to analyze the structure of connected Hopf algebras generated by anti-cocommutative elements and compute the GK dimension of said algebras. Additionally, we apply these results to compare global dimension of connected Hopf algebras and the dimension of their corresponding Lie algebras of primitive elements.

The evolution of the lithospheric mantle beneath Ia Bang, Pleiku plateau, Central Vietnam

Mantle xenoliths are scattered in alkali basalt in central and southern Vietnam. The xenoliths from Ia Bang, Pleiku plateau, consist of fertile spinel lherzolites and refractory spinel harzburgites. The spinel peridotites display varying textures from protogranular through porphyroclastic to equigranular. Primitive mantle-normalized rare earth elements (REE) of clinopyroxene in the peridotites reveal depleted, spoon-shaped, and enriched patterns, suggesting a depletion event followed by various enrichment processes. The correlation between (Yb)n and (Y)n of clinopyroxene in spinel peridotites indicates that the subcontinental lithospheric mantle (SCLM) beneath Ia Bang has been affected by 1–20% fractional melting. The presence of glass and secondary clinopyroxene, coupled with the enrichment of light REEs (LREEs), high field strength elements (HFSEs), and large ion lithophile elements (LILEs) without introductions of new minerals suggests that the xenoliths underwent cryptic metasomatism. Metasomatic agents were identified as Na-alkali silicate, carbonate-rich melts, and H2O-CO2 fluids. The peridotites were at equilibrium temperatures of 841–1131 °C before being brought up by alkali basalt from depths of 36 to 50 km. The SCLM beneath Ia Bang experienced a thinning process in which the refractory lithosphere was thinned and replaced by asthenosphere during the Phanerozoic, following the asthenosphere-lithospheric interaction.

Local index theorem for orbifold Riemann surfaces

We derive a local index theorem in Quillen's form for families of Cauchy-Riemann operators on orbifold Riemann surfaces (or Riemann orbisurfaces) that are quotients of the hyperbolic plane by the action of cofinite finitely generated Fuchsian groups. Each conical point (or a conjugacy class of primitive elliptic elements in the Fuchsian group) gives rise to an extra term in the local index theorem that is proportional to the symplectic form of a new K\"{a}hler metric on the moduli space of Riemann orbisurfaces. We find a simple formula for a local K\"{a}hler potential of the elliptic metric and show that when the order of elliptic element becomes large, the elliptic metric converges to the cuspidal one corresponding to a puncture on the orbisurface (or a conjugacy class of primitive parabolic elements). We also give a simple example of a relation between the elliptic metric and special values of Selberg's zeta function.

Kinetic modeling and optimization of parameters for biomass pyrolysis: A comparison of different lignocellulosic biomass

ABSTRACTA primitive element for the development of sustainable pyrolysis processes is the study of thermal degradation kinetics of lignocellulosic waste materials for optimal energy conversion. The study presented here was conducted to predict and compare the optimal kinetic parameters for pyrolysis of various lignocellulosic biomass such as wood sawdust, bagasse, rice husk, etc., under both isothermal and non-isothermal conditions. The pyrolysis was simulated over the temperature range of 500–2400 K for isothermal process and for heating rate range of 25–165 K/s under non-isothermal conditions to assess the maximum pyrolysis rate of virgin biomass in both cases. Results revealed that by increasing the temperature, the pyrolysis rate was enhanced. However, after a certain higher temperature, the pyrolysis rate was diminished which could be due to the destruction of the active sites of char. Conversely, a decrease in the optimum pyrolysis rate was noted with increasing reaction order of the virgin biomass. Although each lignocellulosic material attained its maximum pyrolysis rate at the optimum conditions of 1071 K and 31 K/s for isothermal and non-isothermal conditions, respectively, but under these conditions, only wood sawdust exhibited complete thermal utilization and achieved final concentrations of 0.000154 and 0.001238 under non-isothermal and isothermal conditions, respectively.

Early Paleoproterozoic (ca. 2.36 Ga) post-collisional granitoids in Yunnan, SW China: Implications for linkage between Yangtze and Laurentia in the Columbia supercontinent

The early Paleoproterozoic is an essential period for understanding the early tectonic evolution of the Yangtze Block and its reconstruction in the Columbia supercontinent, whereas these issues are largely unknown due to the scarce preservation of early Paleoproterozoic geological records. This study presents rarely reported early Paleoproterozoic granitoids from the southwestern Yangtze Block, with integrated studies of zircon U-Pb ages, Lu-Hf isotopic compositions and whole-rock geochemistry. Magmatic zircon U-Pb dating for two monzogranite samples yields weighted mean 207Pb/206Pb ages of 2359 ± 16 Ma and 2363 ± 16 Ma, providing unambiguous evidence for the presence of early Paleoproterozoic magmatism in the Yangtze Block. All the samples have high A/CNK values of 1.30–1.61, typical of S-type granite. These rocks have low total REE contents of 72.5–139.0 ppm with marked enrichment in LREEs ((La/Yb)N = 10.73–23.83) and conspicuously negative Eu anomalies (Eu/Eu* = 0.46–0.55). The rocks exhibit uniform primitive mantle-normalized trace element patterns with enrichment in Rb, Th, U and Pb and depletion in Sr, Nb, Hf and Ti. These dated zircon grains have consistent negative εHf(t) values of −6.2 to −2.8 and TDM2 ages of ca. 2.97–3.16 Ga, indicative of Mesoarchean crustal materials as their magma source. Considering the existence of the ca. 2.36 Ga regional high-grade tectono-metamorphic event, we propose that the ca. 2.36 Ga monzogranites were most likely generated in the early stage of post-collisional extension. Therefore, the southwestern Yangtze Block likely experienced a collision event during ca. 2.40–2.36 Ga, indicative of the involvement of the Yangtze Block in the ca. 2.5–2.3 Ga Arrowsmith orogeny of Laurentia. In addition, a series of accretionary events might also have occurred in the western Yangtze Block before the final assembly of the Columbia supercontinent, implying a tight spatial connection between the Yangtze Block and northwestern Laurentia within this global-scale supercontinent.

Maximal subgroups of the modular and other groups

Abstract In 1933 B. H. Neumann constructed uncountably many subgroups of SL 2 ⁢ ( ℤ ) {{\rm SL}_{2}(\mathbb{Z})} which act regularly on the primitive elements of ℤ 2 {\mathbb{Z}^{2}} . As pointed out by Magnus, their images in the modular group PSL 2 ⁢ ( ℤ ) ≅ C 3 * C 2 {{\rm PSL}_{2}(\mathbb{Z})\cong C_{3}*C_{2}} are maximal nonparabolic subgroups, that is, maximal with respect to containing no parabolic elements. We strengthen and extend this result by giving a simple construction using planar maps to show that for all integers p ≥ 3 {p\geq 3} , q ≥ 2 {q\geq 2} the triangle group Γ = Δ ⁢ ( p , q , ∞ ) ≅ C p * C q {\Gamma=\Delta(p,q,\infty)\cong C_{p}*C_{q}} has uncountably many conjugacy classes of nonparabolic maximal subgroups. We also extend results of Tretkoff and of Brenner and Lyndon for the modular group by constructing uncountably many conjugacy classes of such subgroups of Γ which do not arise from Neumann’s original method. These maximal subgroups are all generated by elliptic elements, of finite order, but a similar construction yields uncountably many conjugacy classes of torsion-free maximal subgroups of the Hecke groups C p * C 2 {C_{p}*C_{2}} for odd p ≥ 3 {p\geq 3} . Finally, an adaptation of work of Conder yields uncountably many conjugacy classes of maximal subgroups of Δ ⁢ ( 2 , 3 , r ) {\Delta(2,3,r)} for all r ≥ 7 {r\geq 7} .

Petrogenesis of the two phases of intrusive rocks at Chodarchay, NW Iran: using trace and rare earth elements

The Chodarchay area is located 50 km east of the city of Zanjan, within the Tarom-Hashtjin subzone, in the Western Alborz structural zone of NW Iran. Igneous rocks in the area include intrusive granitic (phases I and II), and volcanic rocks. Geochemical characteristics of the granitic rocks were determined using their trace and rare earth element (REE) compositions. The phase I intrusive rocks at Chodarchay include quartz monzonite and quartz syenite, while the phase II mainly consists of granite and alkali granite. These intrusive rocks have SiO2 contents ranging between 60.11 and 69.14 wt%, high K2O + Na2O (8.20 to 10.21 wt%) and K2O/Na2O ratios of 1.24 to 2.56. Petrological and geochemical studies indicate that the granitoids have high-K to shoshonitic affinity, they are metaluminous to mildly peraluminous and characterize as I-type granitoids. The investigated granitoids (phases I and II) have fractionated REE patterns characterized by enrichment in light REEs and varying degrees of depletion in heavy REEs. Large-ion lithophile element (LILE) enrichment, high-field strength element (HFSE) depletion, and distinct positive Pb anomaly in the primitive mantle-normalized trace element patterns of the rocks imply subduction-related arc magmatic signatures. It is suggested that the granites formed in a volcanic arc to post-collision setting from a garnet spinel lherzolite source.