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We introduce the notion of D-cyclicity for bounded linear operators on a separable infinite-dimensional complex Banach space, which unifies several classical cyclicity concepts through appropriate choices of D⊂C. We establish fundamental properties of D-cyclic operators, including stability under commuting surjective compositions and invariance under unimodular scalings. For invertible operators, we also show a correspondence between D-cyclicity of T and D[sup.−1]-cyclicity of T[sup.−1], and we prove that the backward shift on ℓ[sup.2](N) is D-cyclic whenever D is unbounded. Moreover, when D is bounded and bounded away from zero, D-cyclic operators exhibit Li–Yorke chaos and satisfy spectral restrictions that exclude adjoint eigenvalues. Furthermore, we prove that if D contains a closed disk around the origin, then a D-cyclic operator admits no non-trivial closed invariant subspace of finite co-dimension.

Let E be an elliptic curve defined over Q and, for a prime p of good reduction for E , let E_p denote the reduction of E modulo p . Inspired by an elliptic curve analogue of Artin’s primitive root conjecture posed by S. Lang and H. Trotter in 1977, J.-P. Serre adapted methods of C. Hooley to prove a GRH-conditional asymptotic formula for the number of primes p x for which the group E_p(F_p) is cyclic. An illuminating proof of this asymptotic formula appeared in a 1983 paper of M. R. Murty, which also established the same unconditionally in the case where E has complex multiplication. More recently, Akbal and Güloğlu considered the question of cyclicity of E_p(F_p) under the additional restriction that p lie in an arithmetic progression. In this paper, we study the question of which arithmetic progressions a n have the property that, for all but finitely many primes p a n , the group E_p(F_p) is not cyclic, answering a question of Akbal and Güloğlu on this issue.

Central Asia is currently a semiarid‐arid region, dominated by the Westerlies. It is important to understand mechanisms of climate and precipitation changes here, as water availability in the region is crucial today and in the future. High‐resolution, absolutely‐dated oxygen isotope (δ18O) records of stalagmites from Kesang Cave characterize a dynamic precipitation history over most of the past 500,000 years. This record demonstrates, for the first time, that climate change in the region exhibits a processional rhythm with abrupt inceptions of low δ18O speleothem growth at times of high Northern Hemisphere summer insolation followed by gradual δ18O increases that track decreases of insolation. These observations and interpretations contrast with the interpretation of nearby, but higher elevation ice core records. The absolutely‐dated caveδ18O shifts can be used to correlate the regional climate variability by providing chronological marks. Combined with other paleoclimate records, the Kesang observations suggest that possible incursions of Asian summer monsoon rainfall or related moisture into the Kesang site and/or adjacent areas during the high insolation times may play an important role in changing orbital‐scale hydrology of the region. Based on our record, arid climate will prevail in this region for the next several millennia, providing that anthropogenic effects do not supersede natural processes. Key Points Speleothem records characterize 500 ka precipitation history in Central Asia Climatic patterns in the Westerlies region are dominated by a precession rhythm Asian Monsoon incursions may explain the hydrological change on precession scale

This article presents novel data from the Nilotic language Dinka, in which the syntax of successive-cyclic movement is remarkably transparent. We show that Dinka provides strong support for the view that long-distance extraction proceeds through the edge of every verb phrase and every clause on the path of movement (Chomsky 1986, 2000, 2001, 2008). In addition, long-distance dependencies in Dinka offer evidence that extraction from a CP requires agreement between v and the CP that is extracted from (Rackowski and Richards 2005, Den Dikken 2009b, 2012a, b). The claim that both of these components constrain long-distance movement is important, as much contemporary work on extraction incorporates only one of them. To accommodate this conclusion, we propose a modification of Rackowski and Richards 2005, in which both intermediate movement and Agree relations between phase heads are necessary steps in establishing a long-distance dependency.

Integrated facies and micropaleontological analyses of the late Piacenzian to early Gelasian, middle shelf to lower shoreface succession of the Strongoli area, southern Italy, reveal a hierarchy of transgressive–regressive sequences. In particular, higher rank sequences up to ca. 40 m thick, composed of transgressive systems tract, highstand systems tracts and falling stage plus lowstand systems tracts, are composed of 10–11 lower rank sequences 2.5–4 m thick. Some micropaleontological parameters were defined: distal/proximal (D/P; ratio between distal and proximal benthic foraminifera); fragmentation (Fr; percentage of fragmentation of benthic foraminifera); P/B (ratio between planktonic and benthic foraminifera); abundance (total count of individuals); diversity (sum of the recognized species). Among these parameters, the D/P and Fr are suitable, if used in conjunction, to recognize uncertainty intervals containing the maximum flooding surface (between the D/P maxima and Fr minima) and the maximum regressive surface (between D/P minima and Fr maxima). Moreover, combining these parameters with the sedimentological evidence, it is possible to recognize transgressive and regressive trends of different hierarchical ranks. The present results are an example illustrating how an integration of different types of data allows the recognition of high-frequency sequences in shelf settings associated with minor shoreline shifts, which would otherwise have been unrecognized on the basis of only one kind of data. The present integrated approach, therefore, provides a way to improve the resolution of sequence stratigraphic analyses.

BackgroundThe psychological risk factors of premenstrual dysphoric disorder (PMDD) are not fully understood, but initial evidence points to a potential role of unfavorable cognitive emotion regulation (ER-) strategies. Given the symptom cyclicity of PMDD, ambulatory assessment is ideally suited to capture psychological and physiological processes across the menstrual cycle. Our study examines habitual ER-strategies in women with PMDD and their predictive value for the course of mood and basal cortisol across the cycle in affected women.MethodsWomen with and without PMDD (n = 61 each) were compared regarding habitual mindfulness, reappraisal, and repetitive negative thinking (RNT). Momentary affect and cortisol output were assessed over two consecutive days per cycle phase (menstrual, follicular, ovulatory, late luteal).ResultsWomen with PMDD reported lower mindfulness, less use of reappraisal and stronger RNT than controls (ps < 0.035). In women with PMDD, higher mindfulness and reappraisal and lower RNT predicted decreased negative and increased positive affect across the menstrual cycle (ps < 0.027). However, women using more favorable ER-strategies displayed stronger mood cyclicity, resulting in stronger mood deterioration in the late luteal phase, thereby resembling women with more unfavorable ER-strategies toward the end of the cycle. Lower mindfulness predicted lower cortisol in the menstrual phase.ConclusionsProtective ER-strategies seem to be generally linked to better momentary mood in women with PMDD, but do not appear to protect affected women from premenstrual mood deterioration. Habitual mindfulness, in turn, seems to buffer blunted cortisol activity in women with PMDD, especially in the menstrual phase.

We give a complete characterization of polynomials in two complex variables that are cyclic with respect to the coordinate shifts acting on Dirichlet-type spaces in the bidisk, which include the Hardy space and the Dirichlet space of the bidisk. The cyclicity of a polynomial depends on both the size and nature of the zero set of the polynomial on the distinguished boundary. The techniques in the proof come from real analytic function theory, determinantal representations for polynomials, and harmonic analysis on curves.

Affective responses to the menstrual cycle vary widely. Some individuals experience severe symptoms like those with premenstrual dysphoric disorder, while others have minimal changes. The reasons for these differences are unclear, but prior studies suggest stressor exposure may play a role. However, research in at-risk psychiatric samples is lacking. In a large clinical sample, we conducted a prospective study of how lifetime stressors relate to degree of affective change across the cycle. 114 outpatients with past-month suicidal ideation (SI) provided daily ratings ( = 6187) of negative affect and SI across 1-3 menstrual cycles. Participants completed the Stress and Adversity Inventory (STRAIN), which measures different stressor exposures (i.e. interpersonal loss, physical danger) throughout the life course, including before and after menarche. Multilevel polynomial growth models tested the relationship between menstrual cycle time and symptoms, moderated by stressor exposure. Greater lifetime stressor exposure predicted a more pronounced perimenstrual increase in active SI, along with marginally significant similar patterns for negative affect and passive SI. Additionally, pre-menarche stressors significantly increased the cyclicity of active SI compared to post-menarche stressors. Exposure to more interpersonal loss stressors predicted greater perimenstrual symptom change of negative affect, passive SI and active SI. Exploratory item-level analyses showed that lifetime stressors moderated a more severe perimenstrual symptom trajectory for mood swings, anger/irritability, rejection sensitivity, and interpersonal conflict. These findings suggest that greater lifetime stressor exposure may lead to heightened emotional reactivity to ovarian hormone fluctuations, elevating the risk of psychopathology.

Organic-rich source rocks are not only crucial for hydrocarbon exploration and production but also serve as valuable archives of past environmental conditions. This study investigates the Upper Cretaceous (Maastrichtian) source rocks present in the Al-Lajoun Basin of central Jordan, to identify geochemical compositional variability corresponding to the paleo-environmental conditions during deposition. To this end, a multifaceted approach using Rock-Eval, SGR, XRD, XRF, ICP-OES, SEM-EDX, and thin-section petrography is utilized to understand bulk organic and inorganic geochemical proxies. Based on the results, the Jordan source rock is characterized as organic-rich, Type IIS kerogen, and thermally immature source rock, representing three distinct cycles of organic matter distribution. Cycle 1 is characterized as organic-rich carbonate mudstones with an average total organic carbon (TOC) content of 17 wt.%. This cycle represents high organic matter productivity, anoxic bottom water conditions, and episodic detrital influx (clays and detrital quartz). Cycle 2 is characterized as silica-rich mudstones to wackestones with an average TOC of 15 wt%. This cycle reflects a shift from carbonate-dominated to silica-dominated biota, likely driven by increased nutrient supply and changing climatic conditions. These conditions resulted in high bioproductivity and highly reducing anoxic/euxinic bottom water conditions during deposition. Cycle 3 represents foraminiferal wackestones to packstones with an average TOC of 12 wt.%. This cycle is characterized by a relatively high detrital sediment input, with comparatively low organic matter productivity and anoxic bottom water conditions. The identified organic and inorganic geochemical variability between these cycles implies changing climatic conditions over the open shelf setting, which in turn implies changes in ocean currents impacting the upwelling system of the Tethys margin. Understanding this relationship between ocean currents, climate, and the geochemical composition is crucial for efficiently exploring and exploiting organic-rich source rocks. A regional correlation of these cycles and their geochemical signatures could provide a powerful tool to trace ocean currents and associated climate change along the Tethys margin during the early Maastrichtian.

The paper considers the properties of the difference equation describing the dynamics of the animal population, obtained earlier in the framework of studies of tundra communities. We have considered a special case in which the model is represented by a one-parameter difference equation that defines a one-dimensional unimodal mapping of a segment into itself, similar to the well-known triangular (tent) mapping, supplemented by a region with a constant value. A change in the mapping parameter generates a bifurcation scenario, in which stability zones arise, characterized by orbits of a constant period, interspersed with zones with more complicated, “quasi-chaotic” regimes. Based on the properties of the n -iterated triangular mapping, a necessary and sufficient condition for the localization of cyclic orbits in the considered type of unimodal mappings is formulated, which makes it possible to identify stability regions for any given period n . On the basis of this condition an algorithm for detecting stability zones is proposed. The main subject of the study is the fractal properties of the set, which is the complement of the obtained set of stability regions to the entire domain of mapping definition. The dynamics of the D H ( n ) value is obtained, the limit of which at n → ∞ is equal to the fractal dimension d H . It is shown that in the studied range of n (2 ≤ n ≤ 22), the D H ( n ) < 0.9, which suggest that d H < 1. If so, then according to the definition of a fractal set, its topological dimension is d T = 0, which means that the complement of the set of stability regions consists of isolated points.