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一个分式型无理不等式的一个推广
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作者 雷冰 《中学数学教学》 2025年第3期93-93,共1页
加拿大数学杂志《Crux Mathematicorum》2024年第4期刊登了由Mihaela Brindeanue提供问题4933.
关键词 mathematical inequalities rational inequalities irrational inequalities
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Pharmacy intervention of irrational medical orders on pharmacy intravenous admixture services of outpatient and emergency departments in Fujian Provincial Hospital 被引量:6
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作者 高红瑾 王少明 +2 位作者 庄捷 陈宇星 米成 《Journal of Chinese Pharmaceutical Sciences》 CAS CSCD 2017年第4期312-316,共5页
In the present study, we aimed to analyze the irrational medical orders and evaluate the effect of pharmacy intervention on pharmacy intravenous admixture services of outpatient and emergency departments in our hospit... In the present study, we aimed to analyze the irrational medical orders and evaluate the effect of pharmacy intervention on pharmacy intravenous admixture services of outpatient and emergency departments in our hospital. The irrational medical orders of PIVAS at the outpatient and emergency departments were retrospectively analyzed in Jun. 2015. We strengthened the pharmacy intervention on irrational medical orders since July 2015. All the cases were selected by systematic sampling method. Cased studied in Jun. 2015 served as the control group, whereas those studied in Jan. 2016 served as the intervention group. The irrational rate and the irrational number of daily average were compared between the control group and intervention group. The common type of irrational outpatient and emergency intravenous orders mainly included irrational use of solvents, irrational dosing interval and inappropriate compatibility of drugs. The irrational rate was reduced from 17.4% to 3.3% (P〈0.01), and the irrational number of daily average was decreased from 5.23 to 1.00 (P〈0.01). Pharmacy intervention can reduce the irrational rate of medical orders in our hospital, which is of great significance to promote rational drug use and improve medical quality. 展开更多
关键词 Irrational medical orders Pharmacy intravenous admixture services Pharmacy intervention
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On Subsets of Q(&radic;<span style="text-decoration:overline;">m</span>) Q under the Action of Hecke Groups H(&lambda;<sub>q</sub>)
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作者 M. Aslam Malik M. Asim Zafar 《Applied Mathematics》 2014年第8期1284-1291,共8页
is the disjoint union of for all , where is the set of all roots of primitive second degree equations , with reduced discriminant equal to k2m. We study the action of two Hecke groups—the full modular group and the g... is the disjoint union of for all , where is the set of all roots of primitive second degree equations , with reduced discriminant equal to k2m. We study the action of two Hecke groups—the full modular group and the group of linear-fractional transformations on . In particular, we investigate the action of on for finding different orbits. 展开更多
关键词 Quadratic irrationals HECKE GROUPS Legendre Symbol G-Set
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Antibiotics/antibacterial drug use, their marketing and promotion during the post-antibiotic golden age and their role in emergence of bacterial resistance 被引量:5
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作者 Godfrey S. Bbosa Norah Mwebaza +2 位作者 John Odda David B. Kyegombe Muhammad Ntale 《Health》 2014年第5期410-425,共16页
During the post-antibiotic golden age, it has seen a massive antibiotic/antibacterial production and an increase in irrational use of these few existing drugs in the medical and veterinary practice, food industries, t... During the post-antibiotic golden age, it has seen a massive antibiotic/antibacterial production and an increase in irrational use of these few existing drugs in the medical and veterinary practice, food industries, tissue cultures, agriculture and commercial ethanol production globally. The irrational drug use has been further exacerbated by the increased marketing and promotion of these drugs by the pharmaceutical companies thus increasing their accessibility in the public and hence their improper use. The lack of production and introduction of the newer and effective antibiotic/antibacterial drugs in clinical practice in the post-antibiotic golden age has seen an increase in the emergence of the resistant pathogenic bacterial infections creating a significant problem in the global health of humankind. The massive productions of the antibiotic/antibacterial drugs have contributed to the poor disposal of these drugs and hence many of them are discharged in various water bodies contributing to the environmental antibiotic/antibacterial drug pollution. In the environment, these drugs exert pressure on the environmental bacteria by destroying useful bacteria that are responsible for the recycling of the organic matter and as well as promoting the selection of the resistant pathogenic bacteria that can spread in human and animal population thus causing an increase in the observed bacterial disease burden and hence a significant global public health problem. The resistant bacterial diseases lead to the high cost, increased occurrence of adverse drug reactions, prolonged hospitalization, the exposure to the second- and third-line drugs like in MDR-TB and XDR-TB that leads to toxicity and deaths as well as the increased poor production in agriculture and animal industry and commercial ethanol production. 展开更多
关键词 Post-Antibiotic GOLDEN Age IRRATIONAL Antibiotic Use Medicines MARKETING and PROMOTION Internet Access ANTIBACTERIAL Resistance
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Bifurcations and chaotic threshold for a nonlinear system with an irrational restoring force 被引量:2
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作者 Tian Rui-Lan Yang Xin-Wei +1 位作者 Cao Qing-Jie Wu Qi-Liang 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第2期136-147,共12页
Nonlinear dynamical systems with an irrational restoring force often occur in both science and engineering, and always lead to a barrier for conventional nonlinear techniques. In this paper, we have investigated the g... Nonlinear dynamical systems with an irrational restoring force often occur in both science and engineering, and always lead to a barrier for conventional nonlinear techniques. In this paper, we have investigated the global bifurcations and the chaos directly for a nonlinear system with irrational nonlinearity avoiding the conventional Taylor's expansion to retain the natural characteristics of the system. A series of transformations are proposed to convert the homoclinic orbits of the unperturbed system to the heteroclinic orbits in the new coordinate, which can be transformed back to the analytical expressions of the homoclinic orbits. Melnikov's method is employed to obtain the criteria for chaotic motion, which implies that the existence of homoclinic orbits to chaos arose from the breaking of homoclinic orbits under the perturbation of damping and external forcing. The efficiency of the criteria for chaotic motion obtained in this paper is verified via bifurcation diagrams, Lyapunov exponents, and numerical simulations. It is worthwhile noting that our study is an attempt to make a step toward the solution of the problem proposed by Cao Q J et al. (Cao Q J, Wiercigroch M, Pavlovskaia E E, Thompson J M T and Grebogi C 2008 Phil. Trans. R. Soe. A 366 635). 展开更多
关键词 nonlinear dynamical system Melnikov boundary irrational restoring force saddle-likesingularity homoclinic-like orbit
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Development of the Irrational Belief Test for Nurses (IBTN): Examination of Reliability and Validity 被引量:3
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作者 Takashi Ohue Michiko Moriyama Takashi Nakaya 《Health》 2015年第3期316-327,共12页
[Purpose]: The purpose of this study is to develop irrational belief test for nurses, and to examine reliability and validity. [Method]: In study 1, The Irrational belief test for nurses was developed based JIBT-20 (m... [Purpose]: The purpose of this study is to develop irrational belief test for nurses, and to examine reliability and validity. [Method]: In study 1, The Irrational belief test for nurses was developed based JIBT-20 (mori et al., 1994) of previous studies. And for the nurse (N = 96, 5 male, 91 female), carried out preliminary investigation, created the provisional version of the Irrational belief test for nurses, and examined factor structure and internal consistency. In study 2, for the nurse (N = 541, 21 male, 520 female) examined validity based on JIBT-20 (Japanese Irrational Belief Test), MBI (Maslach Burnout Inventory), ATQ-R Japanese version (Automatic Thoughts Questionnare-Revised), and for the nurse (N = 91, 3 male, 88 female) examined a test-retest reliability four weeks afterward before long. [Result]: As a result of the explanatory factor analysis by a maximum likelihood estimation and promax rotation, 28-item 7 factors were extracted and was named a “patient belief”, “self-expectation”, “avoidance”, “self-inhibition”, “Ethical blame”, “helplessness”, and “dependence”. Moreover, as a result of conducting confirmation factor analysis, the hypothetical model obtained by explanatory factor analysis fitted (GFI = 0.89, AGFI = 0.86). About the reliability of the measure, a Cronbach’s alpha coefficient is 0.68 - 0.82, and a test-retest reliability is 0.64 and reliability is affirmed. About construct validity was checked correlation with JIBT-20, and about criterion validity was checked the correlation with MBI and ATQ-R Japanese-translation version. [Conclusion]: It is suggested that reliability and validity are verified and the irrational belief test for nurses is a useful measure. The developed test can be used to measure the irrational belief in the context of burnout in nurses. 展开更多
关键词 NURSE IRRATIONAL BELIEF COGNITIVE BEHAVIORAL Therapy
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The Relationship between Dimensions of Emerging Adulthood and Behavioral Problems among Chinese Emerging Adults: The Mediating Role of Physical Activity and Self- Control 被引量:2
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作者 Jin Kuang Jeffrey Jensen Arnett +9 位作者 Erle Chen Zsolt Demetrovics Fabian Herold Rebecca Y.M.Cheung Daniel L.Hall Michaela Markwart Markus Gerber Sebastian Ludyga Arthur F.Kramer Liye Zou 《International Journal of Mental Health Promotion》 2023年第8期937-948,共12页
Emerging adulthood(EA)is a critical stage of life to develop and sustain a healthy lifestyle,which is also a time of vulnerability to poor physical and mental health outcomes.In this study,we conducted a path analysis... Emerging adulthood(EA)is a critical stage of life to develop and sustain a healthy lifestyle,which is also a time of vulnerability to poor physical and mental health outcomes.In this study,we conducted a path analysis(N=1326)to examine associations among four dimensions of EA,levels of regular physical activity(PA),self-control,MPA tendency and irrational procrastination.Results found:1)higher levels of PA predicted both MPA tendency(β=−0.08,95%CI:−0.11 to−0.06,p<0.001)and irrational procrastination(β=−0.01,95%CI:−0.17 to−0.008,p<0.01)indirectly via self-control;2)Instability(β=0.13,95%CI:0.08 to 0.18,p<0.01)and Responsibility(β=−0.06,95%CI:−0.10 to−0.08,p=0.03)exerted direct effects on irrational procrastination and Instability also indirectly predicted irrational procrastination via MPA tendency(β=0.03,95%CI:0.02 to 0.05,p<0.01).These findings proved that perceived features of EA are linked to behavioral problems and supported that regular PA plays a crucial role to protect mental health. 展开更多
关键词 Emerging adulthood Chinese culture physical activity mobile phone addiction irrational procrastination SELF-CONTROL
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Analysis of the periodic solutions of a smooth and discontinuous oscillator 被引量:2
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作者 Zhi-Xin Li Qing-Jie Cao +1 位作者 Marian Wiercigroch Alain Léger 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2013年第4期575-582,共8页
In this paper, the periodic solutions of the smooth and discontinuous (SD) oscillator, which is a strongly irra- tional nonlinear system are discussed for the system having a viscous damping and an external harmonic... In this paper, the periodic solutions of the smooth and discontinuous (SD) oscillator, which is a strongly irra- tional nonlinear system are discussed for the system having a viscous damping and an external harmonic excitation. A four dimensional averaging method is employed by using the complete Jacobian elliptic integrals directly to obtain the perturbed primary responses which bifurcate from both the hyperbolic saddle and the non-hyperbolic centres of the un- perturbed system. The stability of these periodic solutions is analysed by examining the four dimensional averaged equa- tion using Lyapunov method. The results presented herein this paper are valid for both smooth (e 〉 0) and discontin- uous (ce = 0) stages providing the answer to the question why the averaging theorem spectacularly fails for the case of medium strength of external forcing in the Duffing system analysed by Holmes. Numerical calculations show a good agreement with the theoretical predictions and an excellent efficiency of the analysis for this particular system, which also suggests the analysis is applicable to strongly nonlinear systems. 展开更多
关键词 SD oscillator ~ Averaging method. Periodic so-lution ~ Irrational nonlinearity ~ Elliptic integral
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Degradation of dibromophenols by UV irradiation 被引量:1
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作者 Keiko Katayama-Hirayama Naoki Toda +4 位作者 Akihiko Tauchi Atsushi Fujioka Tetsuya Akitsu Hidehiro Kaneko Kimiaki Hirayama 《Journal of Environmental Sciences》 SCIE EI CAS CSCD 2014年第6期1284-1288,共5页
We examined the degradation of dibromophenols (DBPs), i.e. 2,4-DBP, 2,6-DBP and 3,5-DBP by ultraviolet (UV) irradiation and estimated the relationship between degradability and molecular orbital properties of each... We examined the degradation of dibromophenols (DBPs), i.e. 2,4-DBP, 2,6-DBP and 3,5-DBP by ultraviolet (UV) irradiation and estimated the relationship between degradability and molecular orbital properties of each dibromopbenol. The removal of DBPs under a UV lamp system was successfully performed in an aqueous solution. After 5 min of irradiation, the initial DBPs concentration of 20 mg/L was decreased to below 1 mg/L, and about 60% of bromide ion was released. A decrease in the concentration of dissolved organic carbon (DOC) suggested the mineralization of DBPs, The mineralization may occur after release of bromide ions because the decrease of DOC was slower than the release of bromide ions. The degradability of 3,5-DBP was slightly lower than 2,6-DBP and 2,4-DBE Molecular orbital calculation suggested that the electrophilic frontier density and the highest occupied molecular orbital (HOMO) energy may be related to the degradability of DBPs. 展开更多
关键词 bromide ion dibromophenol DOC mineralization UV irration
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Physical Quanta in Quasicrystal Diffraction 被引量:1
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作者 Antony J. Bourdillon 《Journal of Modern Physics》 2021年第12期1618-1632,共15页
Diffraction in quasicrystals is in irrational and geometric series with icosahedral point group symmetry. None of these features are allowed in Bragg diffraction, so a special theory is required. By means of a hierarc... Diffraction in quasicrystals is in irrational and geometric series with icosahedral point group symmetry. None of these features are allowed in Bragg diffraction, so a special theory is required. By means of a hierarchic model, the present work displays exact agreement between an <em>analytic</em> metric, with a <em>numeric </em>description of diffraction in quasicrystals—one that is founded on quasi-structure-factors that are completely indexed in 3-dimensions. At the quasi-Bragg condition, the steady state wave function of incident radiation is used to show how resonant response, in metrical space and time, enables coherent interaction between the periodic wave packet and hierarchic quasicrystal. The quasi-Bloch wave is invariant about all translations<em> <img src="Edit_ce7a6cbd-644e-4811-8416-a6f0c39eb4c3.png" alt="" /></em>, where <img src="Edit_f1f99a28-ba65-4079-aacc-c1b485bc7b16.png" alt="" /> is the quasi-lattice parameter. This is numerically derived, analyzed, measured, verified and complete. The hierarchic model is mapped in reverse density contrast, and matches the pattern and dimensions of phase-contrast, optimum-defocus images. Four tiers in the hierarchy of icosahedra are confirmed, along with randomization of higher order patterns when the specimen foil is oriented only degrees off the horizontal. This explains why images have been falsely described as having “no translational symmetry”. 展开更多
关键词 QUASICRYSTAL ICOSAHEDRA Hierarchic Resonant Response HARMONIC IRRATIONAL Geometric Series METRIC Diffraction Quanta
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Harmony Is Cause—Not Consequence—Of the Quantum 被引量:1
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作者 Antony J. Bourdillon 《Journal of Modern Physics》 2022年第6期918-931,共14页
Einstein claimed Bohr’s theory is incomplete: “the wave function does not provide a complete description of the physical reality” [1]. Their views represent two physics in schism [2] [3]. Quanta are fundamental. Th... Einstein claimed Bohr’s theory is incomplete: “the wave function does not provide a complete description of the physical reality” [1]. Their views represent two physics in schism [2] [3]. Quanta are fundamental. The theory of diffraction in quasicrystals, that is summarized here, is falsifiable and verified. The quanta are not only harmonic;but harmonic in dual series: geometric and linear. Many have believed the quantum is real;rather than conceptual and axiomatic. The quasicrystal proves its reality. 展开更多
关键词 QUASICRYSTAL ICOSAHEDRA Hierarchic Periodic Harmonic IRRATIONAL Geometric Series Metric Resonant Response Dispersion Dynamics
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The Borel measure of sequences with bounded run-length
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作者 Alisa DeStefano Clyde Martin 《Control Theory and Technology》 EI CSCD 2022年第3期316-322,共7页
Infinite sequences defined with a finite alphabet are studied and it is shown that the set of sequences with bounded run-length has measure zero with respect to the Borel measure.Such sequences arise in many applicati... Infinite sequences defined with a finite alphabet are studied and it is shown that the set of sequences with bounded run-length has measure zero with respect to the Borel measure.Such sequences arise in many applications including digitization of certain linear systems involving flows on the circle and 2-torus,large scale simulation,and cryptology.They are basic objects of study in ergodic theory. 展开更多
关键词 DIGITIZATION Borel measure Binary sequences Bounded run-length Irrational flow TORUS
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Intramolecular vibrational dynamical barrier due to extremely irrational couplings
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作者 区树清 吴国祯 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第10期2952-2956,共5页
The intramolecular vibrational dynamics due to extremely irrational couplings is demonstrated by contrast to the resonance couplings, for the three-mode case of H2O as an example. The extremely irrational couplings ar... The intramolecular vibrational dynamics due to extremely irrational couplings is demonstrated by contrast to the resonance couplings, for the three-mode case of H2O as an example. The extremely irrational couplings are shown to impose such strong hindrance to intramolecular vibrational relaxation (IVR) that they act as barriers. They restrict the direct action/energy transfer between the two stretching modes, though they allow the transfer between a stretching and a bending modes. In contrast, the resonance is more mediated by the bending mode and leads to chaotic IVR. It is also shown that there is a region in the dynamical space in which resonance and extremely irrational couplings coexist. 展开更多
关键词 intramolecular vibrational relaxation extremely irrational couplings resonance
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Medicine prescription practices of homeopathic undergraduate students in West Bengal,India
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作者 Subhranil Saha Munmun Koley +6 位作者 Jogendra Singh Arya Gurudev Choubey Shubhamoy Ghosh Subhasish Ganguly Aloke Ghosh Sangita Saha Malay Mundle 《Journal of Integrative Medicine》 SCIE CAS CSCD 2014年第1期7-12,共6页
OBJECTIVE: To our knowledge, prescription of homeopathic medicines by homeopathic undergraduate students has not been studied before though it may possess serious implications. We aimed to determine the practice and ... OBJECTIVE: To our knowledge, prescription of homeopathic medicines by homeopathic undergraduate students has not been studied before though it may possess serious implications. We aimed to determine the practice and attitudes of prescription by homeopathic undergraduate students. METHODS: A cross-sectional study was carried out involving all the students from four government homeopathic schools of West Bengal, India. Ethical requirements were ensured and data were collected using self-administered questionnaires. Chi-square tests and logistic univariate regression analyses were performed to identify associations and differences. RESULTS: A total of 328 forms were completed. Of these, 264 (80.5%) homeopathic undergraduate students admitted of prescribing medicines independently and most (40.5%) said that they did this 2-3 times a year. The most common reasons for this were 'urgency of the problem' (35.2%), 'previous experience with same kind of illness' (31.8%), and 'the problem too trivial to go to a doctor' (25.8%). About 63.4% of the students thought that it was alright to independently diagnose an illness while 51.2% thought that it was alright for them to prescribe medicines to others. Common conditions encountered were fever, indigestion, and injury. Students who prescribed medicines were more likely to belong to Calcutta Homeopathic Medical College and Hospital (odds ratio = 5.8; 95% confidence interval 2.247-14.972). Prescription by students gradually increased with academic years of homeopathic schools. Many students thought it was alright for students to diagnose and treat illnesses. CONCLUSION: Prescription of medicines by homeopathic undergraduate students is quite rampant and corrective measures are warranted. 展开更多
关键词 HOMEOPATHY education medical undergraduate INDIA prescriptions drug practice institutional drug use irrational
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Self-Medication among Adults in Minia, Egypt: A Cross Sectional Community-Based Study
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作者 Eman R. Ghazawy 《Health》 2017年第6期883-895,共13页
Self-medication may be associated with side effects and increases the chance of drug interactions and also affects the adherence to treatment and quality of life. This study aims at determining the pattern of self-med... Self-medication may be associated with side effects and increases the chance of drug interactions and also affects the adherence to treatment and quality of life. This study aims at determining the pattern of self-medication, identifying knowledge, attitude and self-reported practices concerning the usage of the drugs and identifying demographic factors that could influence self-medication practices among the general population in El-Minia, Egypt. A community-based cross-sectional study was conducted among 422 randomly selected adults using a multi-stage random sampling technique. Data were collected by using a structured interview questionnaire. Respondents who had practiced some sort of self-medication during the past month were 73% of the sample. The commonest cause of self-medication, illness, was perceived as minor (59.7%). The most common perceived illness for self-medication was common cold (90.6%). Older respondents (>40 years) were about twice more likely to practice self-medication than younger ones. Similarly, professionals in their work were 3.4 times more likely to practice self-medication than unemployed individuals. Self-medication is a relatively frequent problem in Minia and interventions at different levels are required. 展开更多
关键词 SELF-MEDICATION El-Minia CROSS-SECTIONAL IRRATIONAL ANTIBIOTICS
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Continued Fractions and Dynamics
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作者 Stefano Isola 《Applied Mathematics》 2014年第7期1067-1090,共24页
Several links between continued fractions and classical and less classical constructions in dynamical systems theory are presented and discussed.
关键词 Continued FRACTIONS Fast and SLOW Convergents IRRATIONAL ROTATIONS Farey and GAUSS Maps Transfer Operator Thermodynamic FORMALISM
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Synergetics as a Positivistic "Trick" for Philosophy
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作者 Salahaddin Khalilov 《Journal of Philosophy Study》 2012年第1期27-34,共8页
This paper substantiates the idea that particular science reflects only a certain angle of a complex model of the world. Guidance as to "adding" particular science data in order to achieve a holistic picture of the ... This paper substantiates the idea that particular science reflects only a certain angle of a complex model of the world. Guidance as to "adding" particular science data in order to achieve a holistic picture of the world is a philosophical outlook. The meaning of each relatively closed system is revealed only in the context of a more capacious system. According to the author, as the material world itself, its epistemic models as well are built according to the principle of "matryoshka dolls." The rational and irrational are discussed in the paper as equal moments of scientific knowledge. Contrary to the importance given to randomness in synergy, the author considers if it is possible to find out the causes of all events. In order to do this, other viewpoints and structure levels should be considered. There is a hidden order in every chaos, and that is revealed only in a certain situation. The main issue is taking into account the counter action of the system with the environment. 展开更多
关键词 chaos SYNERGETICS RANDOMNESS RATIONAL IRRATIONAL
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The Influences of American Deep Image on the Third-Generation Poets in China
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作者 YIN Gen-de 《Journal of Literature and Art Studies》 2017年第10期1251-1257,共7页
The Third-Generation Poetry of China (namely Post-misty Poetry too) initiated with the introduction of Western modernist poetry, especially sorts of American Post-modernist poetry schools into China. "The relation ... The Third-Generation Poetry of China (namely Post-misty Poetry too) initiated with the introduction of Western modernist poetry, especially sorts of American Post-modernist poetry schools into China. "The relation between American poetry and Chinese poetry has a long history, which lies in the influences on the creation of the Third-Generation poets. This influence is probably unprecedented in its depth and breadth." "Irrational association" and "leaping images" proposed by American Deep Image poets influenced by Freudian and Jungian unconscious perception gained an extraordinary appreciation among the Third-Generation poets who were in pursuit constantly of the experiments on poetic form and language. This paper mainly discusses the influences of American Deep Image on the Third-Generation poets of China through a case study of WANG Yin and CHEN Dongdong's poems. 展开更多
关键词 The Third-Generation Poetry Deep Image influence irrational association leaping image
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Analysis on Irrational Decision Making of Tobacco Family Farmers from the Perspective of Optimal Scale of Efficiency
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作者 Ya nan SUN Lulu CUI Baohua YU 《Asian Agricultural Research》 2022年第9期7-11,15,共6页
The larger the difference between the willingness scale of tobacco family farmers and the optimal scale of efficiency,the greater the degree of irrationality,and the higher the decision making risk.With the aid of DEA... The larger the difference between the willingness scale of tobacco family farmers and the optimal scale of efficiency,the greater the degree of irrationality,and the higher the decision making risk.With the aid of DEA model,this study calculated the optimal scale of efficiency of Guiyang tobacco family farms.Using the ratio of willingness scale and efficiency optimal scale,it measured the degree of irrationality of family farmers.In addition,with the help of multiple linear regression model,it explained the irrational decision making mechanism of family farmers.Finally,it made a portrait of farmers who tend to make irrational decisions,to find specific farmers and guide them in their production and operation,reduce the risk of planting scale decision making and stabilize the sustainable development of the tobacco industry. 展开更多
关键词 Irrational decision making Family farmers Optimal scale of efficiency PORTRAIT
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A History, the Main Mathematical Results and Applications for the Mathematics of Harmony
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作者 A. P. Stakhov 《Applied Mathematics》 2014年第3期363-386,共24页
We give a survey on the history, the main mathematical results and applications of the Mathematics of Harmony as a new interdisciplinary direction of modern science. In its origins, this direction goes back to Euclid... We give a survey on the history, the main mathematical results and applications of the Mathematics of Harmony as a new interdisciplinary direction of modern science. In its origins, this direction goes back to Euclid’s “Elements”. According to “Proclus hypothesis”, the main goal of Euclid was to create a full geometric theory of Platonic solids, associated with the ancient conception of the “Universe Harmony”. We consider the main periods in the development of the “Mathematics of Harmony” and its main mathematical results: algorithmic measurement theory, number systems with irrational bases and their applications in computer science, the hyperbolic Fibonacci functions, following from Binet’s formulas, and the hyperbolic Fibonacci l-functions (l = 1, 2, 3, …), following from Gazale’s formulas, and their applications for hyperbolic geometry, in particular, for the solution of Hilbert’s Fourth Problem. 展开更多
关键词 Golden Ratio Pascal’s Triangle and FIBONACCI NUMBERS Binet’s FORMULAS Gazale’s FORMULAS Hyperbolic FIBONACCI Functions Number Systems with IRRATIONAL Bases FIBONACCI λ-Numbers “Metallic Proportions” Hilbert’s Fourth Problem
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