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The Gaussian \( q \)-distribution is a generalization of the traditional Gaussian (normal) distribution that incorporates the concept of non-extensivity and is part of the broader family of distributions used in q-statistics (also known as Tsallis statistics). This distribution arises in contexts where systems exhibit long-range correlations and is used to describe phenomena that cannot be accurately characterized by the standard Gaussian distribution due to the presence of heavy tails or other non-standard features.

A Lambert series is a type of mathematical series named after the mathematician Johann Heinrich Lambert. It is defined in a particular form, usually involving a power series with specific coefficients. The general form of a Lambert series can be expressed as: \[ \sum_{n=1}^{\infty} \frac{n q^n}{1 - q^n} \] where \( |q| < 1 \) is a complex variable.

Mock modular forms are a type of mathematical function that generalize the concept of modular forms. They arise in number theory and have connections to various areas, including combinatorics, topology, and mathematical physics. ### Background A **modular form** is a complex function that satisfies certain transformation properties under the action of a subgroup of the modular group, along with specific growth conditions at infinity.

The \( Q \)-Pochhammer symbol, often denoted as \( (a;q)_n \), is a notation used in the area of q-series and q-special functions. It is a generalization of the standard Pochhammer symbol.

David Evans is an Australian mathematician and engineer known for his contributions to numerical methods, computational mathematics, and particularly for his work in the field of wave propagation and acoustics. He has been involved in research and development related to mathematical models and simulation techniques that find applications in various engineering fields, such as telecommunications and materials science. Evans has published numerous papers in scientific journals and has contributed to the advancement of methods that solve complex engineering problems using mathematical frameworks.

The just-noticeable difference (JND), also known as the difference threshold or the minimal detectable difference, refers to the smallest change in a stimulus that can be detected by a sensory system. It represents the minimum amount of change that a person can perceive between two stimuli. The concept of JND is rooted in psychophysics, a field of study that examines the relationship between physical stimuli and the sensations and perceptions they produce.

Mathematical and Statistical Psychology journals are academic publications that focus on the intersection of mathematics, statistics, and psychology. They typically cover a range of topics that deal with the application of mathematical and statistical methods to psychological research, including the development and testing of psychological theories, the analysis of psychological data, and the construction of models to represent psychological phenomena.

Psychological methodology refers to the techniques and principles researchers use to investigate psychological phenomena systematically. It encompasses the strategies, tools, and procedures that guide research design, data collection, analysis, and interpretation in the field of psychology. Here are some key components of psychological methodology: 1. **Research Design**: This includes the overall strategy that a researcher employs to integrate the different components of a study in a coherent and logical way. Common designs include experiments, correlational studies, longitudinal studies, and case studies.

Quantitative psychologists are specialists within the field of psychology who focus on the development and application of statistical and mathematical methods to understand psychological phenomena. Their work encompasses a variety of tasks, including: 1. **Research Design:** They design experiments and studies that systematically test psychological theories and hypotheses. 2. **Data Analysis:** Quantitative psychologists utilize statistical techniques to analyze data collected from psychological research, helping to determine relationships, effects, and patterns.

Psychological research methods are systematic approaches used to investigate psychological phenomena, gather data, and analyze information. Here’s a list of some common psychological research methods: 1. **Experimental Methods**: - **Laboratory Experiments**: Conducted in a controlled environment where variables can be manipulated. - **Field Experiments**: Research conducted in a natural environment where variables are manipulated but the setting is not controlled by the researcher.

AM1* (also referred to as AM1 or Austin Model 1) is a semi-empirical quantum chemistry method used for molecular modeling and calculations. It's an extension of the original AM1 method, which was developed to provide a balance between computational efficiency and accuracy for large molecules, particularly organic compounds. The AM1 method simplifies the quantum mechanical calculations by using empirical parameters derived from experimental data, allowing for the approximation of molecular orbitals and electronic structures.

"Tell Me What You See" is a book by the Australian author and art historian, Christine D. H. Dunn. Published in 2022, it delves into the intricate relationship between art and perception. The book encourages readers to engage with art in a more profound way by reflecting on their interpretations and emotional responses to various artworks. Dunn’s work often explores themes of observation and interpretation, prompting readers to consider how their personal experiences and cultural backgrounds influence their understanding of art.

The Haldane–Shastry model is an important theoretical model in condensed matter physics, particularly in the study of quantum magnetism and lattice systems. Named after physicists F.D.M. Haldane and B.S. Shastry, who contributed to its development, the model describes a one-dimensional system of spin-1/2 particles arranged on a lattice with specific interactions.

The Gaudin model is a mathematical framework in the field of statistical mechanics and quantum integrable systems. Named after the physicist Michel Gaudin, the model originally describes a system of one-dimensional quantum spins or particles that interact with each other. It is particularly known for its integrability and the presence of rich mathematical structures.

Edmund Alfred Cornish (1834–1914) was a notable British painter and engraver recognized for his landscapes and genre scenes. He was associated with the Pre-Raphaelite movement and is known for his detailed and vibrant style. His work often captured the beauty of the English countryside and domestic life.

Nikolai Aleksandrovich Kozyrev (1908-1983) was a Soviet astronomer and physicist, known primarily for his work in astrophysics and for his controversial theories on the nature of time and space. He became notable for his research on the potential for physical effects arising from the gravitational influence of celestial bodies and for his hypothesis concerning the relationship between time and physical processes.

The odor detection threshold is the minimum concentration of a substance that can be detected by the human sense of smell. It is the lowest level at which a particular odor can be perceived, and it can vary widely depending on the substance, the individual's sensitivity, and environmental factors. In scientific studies, the odor detection threshold is often quantified in terms of parts per million (ppm), milligrams per cubic meter (mg/m³), or other relevant units, depending on the context.

Sensometrics is a field that combines sensory science, statistics, and multivariate data analysis to analyze and interpret sensory data. It focuses on the measurement and modeling of sensory perceptions, typically related to food, beverages, cosmetics, and other products where human sensory experiences (like taste, smell, texture, and appearance) are critical for evaluation and quality control. Sensometrics employs various statistical techniques to assess consumer preferences, sensory attributes, and product characteristics.

Sensory analysis is a scientific method used to evaluate and measure the sensory properties of products, particularly food and beverages, based on human perception. It involves using the senses—such as taste, smell, sight, touch, and hearing—to assess the attributes and quality of a product. This analysis can help in understanding how consumers perceive a product and can guide product development, quality control, and marketing strategies.

The sensory threshold refers to the minimum level of stimulus intensity that can be detected by the sensory organs and perceived by the brain. This concept is critical in psychology and neuroscience as it helps to understand how organisms interact with their environment. There are two main types of sensory thresholds: 1. **Absolute Threshold**: This is the smallest amount of stimulus energy that can be detected at least 50% of the time.