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Research Experience for Undergraduates (REU)
Life After Ursinus
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Mathematics and Computer Science Courses
CS-010. Computational Problem Solving
This workshop course offers a structured environment for helping students become better and more efficient computational problem-solvers. Focus is on the rapid development of software for solving hard problems. May be repeated for credit. Prerequisite: CS-173 or equivalent experience. Graded S/U. Three hours per week. One semester hour.
CS-170 Q. In Silico, Designing Simulations via Computer Science
An introduction to computer science as a tool for analyzing and working with scientific data, and simulating experiments. The course introduces Python and studies its application in various scientific domains including Bioinformatics, Environmental Studies, Chemistry, Physics and Imaging by looking at a variety of problems drawn from these domains. The lab will involve the implementation of algorithms and analysis on data sets drawn from these areas. No prior programming experience is assumed. Offered every Fall. Three hours of lecture and two hours of laboratory per week. Four semester hours. (S, R.)
Note: CS-170Q may not be used as elective credits for computer science majors or minors.
CS-173. Introduction to Computer Science
Introduction to the field of computer science. Topics include: methods for computational problem solving, algorithm development techniques, processes for development of new technologies, and programming projects of increasing complexity in a high-level language with emphasis on good programming style. The course also includes exposure to advanced topics in computer science such as graphics, human-computer interaction, and software engineering. Recommended for students in mathematics; business and economics; and the natural sciences. No prior computer programming experience is assumed. Offered every semester. Three hours of lecture and one hour of laboratory per week. Four semester hours. (Q, R.)
CS-174. Object-Oriented Programming
A continuation of CS-173. More detailed exploration of classes and instances, and an introduction to collection classes such as vectors, lists, maps and sets. Larger programs and/or team projects. Prerequisite: A grade of C– or higher in CS-173. Offered every semester. Three hours of lecture and one hour of lab per week. Four semester hours. (R.)
CS-274. Computer Architecture and Organization
Hierarchical structure of computer architecture, number systems, arithmetic operations, codes, switching algebra, logic gates, assembly language programming. Prerequisite: CS-174. Offered in the spring semester. Three hours of lecture and one hour of laboratory per week. Four semester hours.
CS-275. Software Engineering
Topics integral to the design, implementation and testing of a medium-scale software system combined with the practical experience of implementing such a project as a member of a programming team. Use of the Unified Modeling Language (UML) for software design. Prerequisite: A grade of C– or higher in CS-174. Offered in the fall semester. Three hours per week. Four semester hours. (Q.)
CS-350. Oral Presentation
A computer science oral presentation. This course will satisfy the College requirement for an oral presentation in the major. Prerequisite: written consent of a department faculty member. Graded S/U. Zero semester hours.
Note: This course is usually taken in conjunction with internships (CS-381, 383) and research/independent work (CS-391-394, 491, 492).
CS-371W. Data Structures and Algorithms
Introduction to algorithm analysis and data structures. Complexity of algorithms, analyzing basic data structure operations, searching and sorting algorithms, tables, hashing, recursion, tree and graph algorithms. Prerequisites: MATH-111 or equivalent, MATH-236W, and CS-275, or permission of the instructor. Offered in the spring semester. Three hours per week. Four semester hours.
CS-373. Theory of Computation
Principles of formal languages, automata, computability and computational complexity. Emphasis on writing proofs of theorems. Prerequisites: MATH-236W, a grade of C– or higher in CS-174. Offered in the fall of odd years. Three hours per week. Four semester hours.
CS-374. Principles of Programming Languages
Syntax, processors, representations and styles of programming languages. Study and comparison of several modern programming languages. Prerequisite: A grade of C– or higher in CS-174. Offered in the spring of odd years. Three hours per week. Four semester hours.
CS-376. Operating Systems
Fundamental concepts of operating systems. Sequential processes, concurrent processes, resource management, scheduling, synchronization, file systems, and computer security. Projects include writing of a program to simulate major components of an operating system. Pre- or co-requisite: CS-274. Offered in the spring of even years. Three hours per week. Four semester hours.
CS-377. Database Design
The concepts involved in designing and using a database management system. Logical and physical database design. Entity-Relational Modeling. Various types of database structures, manipulations of a database structure through applications, query techniques, and programming in a database language. Prerequisite: CS-275. Offered in the fall of odd years. Three hours per week. Four semester hours.
CS-381. Internship
An off-campus academic/work experience under the supervision of an internship adviser and an on-site supervisor. An oral presentation to the department is required. Contact the chair of the department for further details. Open to juniors and seniors. The term during which the internship work is performed will be noted by one of the following letters, to be added immediately after the internship course number: A (fall), B (winter), C (spring), or D (summer). Internships undertaken abroad will be so indicated by the letter I. The intern must complete a minimum of 120 hours of work. Graded S/U. Prerequisites: three courses in computer science and approval of a faculty internship adviser. Three semester hours. (XLP.)
An off-campus academic/work experience under the supervision of an internship adviser and an on-site supervisor. An oral presentation to the department is required. Contact the chair of the department for further details. Open to juniors and seniors. The term during which the internship work is performed will be noted by one of the following letters, to be added immediately after the internship course number: A (fall), B (winter), C (spring), or D (summer). Internships undertaken abroad will be so indicated by the letter I. The intern must complete a minimum of 160 hours of work. Graded S/U. Prerequisites: three courses in computer science and approval of a faculty internship adviser. Four semester hours. (XLP.)
Note: Students may receive credit for two internships that meet the conditions described in this catalogue.
CS-391. Research/Independent Work
Independent investigation of an area of computer science not covered in regular courses. Prerequisite: Written consent of a department faculty member. Graded S/U. One semester hour.
Note: This course may be taken more than once.
Independent investigation of an area of computer science not covered in regular courses. Prerequisite: Written consent of a department faculty member. Graded S/U. Two semester hours.
CS-394. Independent Study
Independent investigation of an area of computer science not covered in regular courses. Prerequisite: Written consent of a department faculty member. An oral presentation to the department is required. Four semester hours. (XLP.)
Note: This course may be taken more than once. This course always fulfills the ILE requirement for the college, but may satisfy an elective requirement for the major only with prior permission of the department chair
CS-471. Seminar in Computer Science I
A detailed study of an advanced topic in computer science, such as computational geometry, compilers, data mining, robotics or distributed technology. Prerequisites: CS-275 or written permission of the instructor. Usually offered in the fall semester of even years. May be repeated for credit. Three hours per week. Four semester hours.
CS-472. Seminar in Computer Science II
The course will cover topics similar to those listed in CS-471. Prerequisites: CS-275 or written permission of the instructor. Offered in the spring semester as needed. May be repeated for credit. Three hours per week. Four semester hours.
CS- 474. Human-Computer Interaction
The study of human-computer interaction enables system architects to design useful, efficient, and enjoyable computer interfaces. This course teaches the theory, design procedure, and programming practices behind effective human interaction with computers. This course satisfies the College requirement for a capstone experience in the major. Prerequisite: CS-275. Offered in the spring semester of even years. Three hours per week. Four semester hours.
CS- 475. Computer Networks
Architecture and protocols of computer networks. Protocol layers; network topology; data-communication principles, including circuit switching, packet switching and error control techniques; sliding window protocols, protocol analysis and verification; routing and flow control; local and wide area networks; network interconnection; client-server interaction; emerging networking trends and technologies; topicsin security and privacy. This course will satisfy the College requirement for a capstone experience in the major. Prerequisite or co-requisite: CS-274. Offered in the spring of odd years. Three hours per week. Four semester hours.
CS- 476. Computer Graphics
Software and hardware for interactive computer graphics. Implementation of device drivers, 3-D transformations, clipping, perspective, and input routines. Data structures, hidden surface removal, color shading techniques, and some additional topics will be covered. This course will satisfy the College requirement for a capstone experience in the major. Prerequisites: CS-275 and MATH-235. Offered fall of even years. Three hours per week. Four semester hours.
CS- 477. Artificial Intelligence
This course explores principles and methods for knowledge representation, reasoning, learning, problem solving, planning, heuristic search, and natural language processing. These principles are applied to problems which require building intelligent systems in a variety of domains. This course will satisfy the College requirement for a capstone experience in the major. Prerequisite: CS-275. Offered in fall of odd years. Three hours per week. Four semester hours.
Independent research in computer science. This course is appropriate for students pursuing departmental honors and distinguished honors projects, and is open to other students interested in research in computer science. An oral presentation to the department is required. Prerequisites: Written consent of a member of the faculty to serve as an advisor. Four semester hours. (XLP.)
CS-492W. Research/Independent Work
Independent research in computer science. This course serves as the culminating course for departmental honors and distinguished honors projects. This course will satisfy the college requirement for a capstone experience in the major. Prerequisites: CS-491, meets college and departmental requirements for honors, and written consent of a member of the faculty to serve as an advisor. Four semester hours. (XLP.)
MATH-010. Problem-Solving
A structured seminar, focusing on problem-solving. Students are encouraged to work collaboratively and individually on challenging mathematical problems that are presented without the context of techniques from a specific course. Problem-solving skills are enhanced, through using higher level thinking and applying techniques to different problem types. Problems in the fall semester include those from past Putnam exam while in the spring semester problems are drawn largely from professional journals. May be repeated for credit. Graded S/U. Three hours per week. One semester hour.
MATH-100. Mathematics for the Liberal Arts
A cultural and historical approach to mathematics. Appreciation of the beauty and creative aspects of mathematics and its role in nature and the arts. Essay tests and papers as well as problems using deductive reasoning. Offered in the spring semester. Three hours per week. Four semester hours. (R.)
MATH-110. Precalculus
A review of algebraic, exponential and logarithmic functions, Cartesian plane, circular, trigonometric and inverse trigonometric functions. Use of a computer algebra system. This course prepares students for MATH-111. Prerequisite: Placement based on the high school record and a placement test. Offered in the fall semester. Four hours per week. Four semester hours. (R.)
Note: A student who has received credit for MATH-105 or 111 may not enroll in MATH-110.
MATH-111. Calculus I
Limits; derivatives; applications of derivatives; trigonometric, inverse trigonometric, logarithmic, and exponential functions; applications of these functions; indeterminate forms; the Fundamental Theorem of Calculus. Use of a computer algebra system. Prerequisite: Placement based on the high school record and a placement test, or a grade of C- or better in MATH-110. Offered both semesters. Four hours per week. Four semester hours. (R, Q.)
Note: A student who has received credit for MATH-111 may not enroll in MATH-110
MATH-112. Calculus II
A continuation of MATH-111.Techniques of integration, applications of integration, improper integrals, polar coordinates, parametric equations, infinite sequences and series. Use of a computer algebra system. Prerequisite: Placement based on the high school record and a placement test, or a grade of C- or better in MATH-111. Offered both semesters. Four hours per week. Four semester hours. (R, Q.)
MATH-211. Multivariable Calculus
Functions of several variables, including three-dimensional geometry and vectors, space curves and motion in space, partial differentiation, multiple integration, line and surface integrals, and the theorems of Green, Gauss, and Stokes. Use of a computer algebra system. Prerequisite: A grade of C- or better in MATH-112, or permission of the department. Offered both semesters. Four hours per week. Four semester hours. (R, Q.)
MATH-235. Linear Algebra
Systems of linear equations, matrix algebra, vector spaces, linear transformations, eigenvectors and eigenvalues, inner products and orthogonality, applications. The computer as a computational tool. Prerequisite: MATH-112 or equivalent, or permission of the instructor. Offered in the fall semester. Four hours per week. Four semester hours. (R.)
MATH-236W. Discrete Mathematics
A course designed to bridge the gap between computation-oriented introductory courses and proof-oriented advanced courses. The language of contemporary mathematics, including the proper way to write mathematics, and the nature of mathematical reasoning. Extensive writing projects. Topics studied may include axiomatic systems, logic, set theory, functions, mathematical induction, graph theory and trees, permutations and combinations. Prerequisite: MATH-111, placement or permission of the instructor. Offered in the spring semester. Three hours per week. Four semester hours. (R.)
MATH/PHIL-260. Logic
An introduction to the concepts and techniques used in symbolic reasoning, primarily through the study of first-order logic, the translation of sentences of ordinary English into a formal language, and the construction of derivations. Topics include: formalization, proofs, mathematical induction, propositional and predicate logic, quantifiers, and sets. (Formerly PHIL-202.) Three hours per week. Four semester hours. (R.)
Note: Students who have received credit for MATH-236W or the former PHIL-202 may not enroll in MATH/PHIL 260.
MATH-310. Differential Equations and Mathematical Models
Mathematical methods for developing models in the physical, biological, and social sciences. Emphasis on models involving differential equations. Solutions, visualizations, and interpretations of first order, second order, and systems of linear and non-linear differential equations. Numerical, graphical and analytic methods, with extensive qualitative analysis approaches. Laplace transforms. Independent projects. Additional topics chosen from forcing and resonance, discrete dynamical systems, and power series solutions. Use of a computer algebra system. Prerequisite: MATH-211. Offered in the spring semester. Three hours per week. Four semester hours.
MATH-311W. Analysis I
An introduction to the real number system and set operations; theoretical treatment of supremum, infimum, countability, sequences, limits, continuity, and differentiability. Additional topics may include series, structure of point sets and abstract metric spaces. Emphasis on writing mathematical proofs. Prerequisite: MATH-211 and 236W. Offered in the fall semester. Three hours per week. Four semester hours.
MATH-312. Analysis II
A continuation of MATH-311. The Riemann and Riemann-Stieltjes integral; infinite series, sequences and series of functions; introduction to metric spaces. Additional topics may include Lebesgue measure and integration, orthogonal functions and Fourier series. Prerequisite: MATH-311. Offered as needed.Three hours per week. Four semester hours. (R.)
MATH-322. Modern Geometry
Topics in Euclidean and non-Euclidean geometry, including some of the following: geometry from an axiomatic viewpoint, synthetic Euclidean geometry, transformation geometry and symmetry, affine and projective geometry, inversive geometry, spherical geometry, and hyperbolic geometry. Prerequisites: MATH-235 and 236W, or permission of the instructor. Offered in the spring of odd years. Three hours per week. Four semester hours. (R.)
MATH-335. Abstract Algebra
An introduction to algebraic structures, with emphasis on groups: Subgroups, quotient groups, homomorphisms, isomorphism theorems, Cayley's theorem, permutation groups. An introduction to the theory of rings. Additional topics may include: series of groups, free groups, and the Sylow theorems. Prerequisites: MATH-235 and 236W. Offered in the spring semester. Three hours per week. Four semester hours.
MATH-336. Abstract Algebra II
An introduction to algebraic structures, with emphasis on rings: subrings, ideals, quotient rings, homomorphisms, isomorphism theorems, integral domains, unique factorization domains, Euclidean domains. Additional topics may include: fields and field extensions, Galois theory. Prerequisite: MATH-335. Offered in the fall of odd years. Three hours per week. Four semester hours. (R.)
MATH-341. Probability
An introduction to probability theory, discrete and continuous probability distributions, moments and moment-generating functions of random variables, and transformations of random variables. Prerequisite: MATH-211. Offered in the fall semester. Four hours per week. Four semester hours.
MATH-350. Oral Presentation
A mathematics oral presentation. This course will satisfy the College requirement for an oral presentation in the major. Prerequisite: written consent of a department faculty member. Graded S/U. Zero semester hours.
Note: This course is usually taken in conjunction with internships (MATH-381, 383, 384, 441) and research/independent work (MATH-391-394, 441, 491, 492W).
MATH-361. Graph Theory
Elements of graph theory, including the study of Eulerian graphs, planar graphs, trees, connectivity, colorings, algorithms, domination, and the applications of graphs to computer science. Prerequisite: MATH-236W. Offered in the fall semester of even years. Three hours per week. Four semester hours.
MATH-381. Internship
An off-campus academic/work experience under the supervision of an internship adviser and an on-site supervisor. An oral presentation to the department is required. Contact the chair of the department for further details. Open to juniors and seniors. The term during which the internship work is performed will be noted by one of the following letters, to be added immediately after the internship course number: A (fall), B (winter), C (spring), or D (summer). Internships undertaken abroad will be so indicated by the letter I. The intern must complete a minimum of 120 hours of work. Graded S/U. Prerequisites: three courses in mathematics and approval of faculty internship adviser. Three semester hours. (XLP.)
An off-campus academic/work experience under the supervision of an internship adviser and an on-site supervisor. An oral presentation to the department is required. Contact the chair of the department for further details. Open to juniors and seniors. The term during which the internship work is performed will be noted by one of the following letters, to be added immediately after the internship course number: A (fall), B (winter), C (spring), or D (summer). Internships undertaken abroad will be so indicated by the letter I. The intern must complete a minimum of 160 hours of work. Graded S/U. Prerequisites: three courses in mathematics and approval of faculty internship adviser. Four semester hours. (XLP.)
MATH-391. Research/Independent Work
Independent investigation of an area of mathematics not covered in regular courses. Prerequisite: Written consent of a department faculty member. Graded S/U. One semester hour.
Independent investigation of an area of mathematics not covered in regular courses. Prerequisite: Written consent of a department faculty member. Graded S/U. Two semester hours.
MATH-394. Independent Study
Independent investigation of an area of mathematics not covered in regular courses. An oral presentation to the department is required. Prerequisite: Written consent of a department faculty member. Four semester hours. (XLP.)
Note: This course may be taken more than once. This course always fulfills the ILE requirement for the college, but may satisfy an elective requirement for the major only with prior permission of the department chair.
MATH-411. Complex Analysis
Complex numbers; polar representation; stereographic projection; the exponential and logarithm functions; analytic functions; the Cauchy-Riemann Equations; fractional linear transformations; Cauchy's integral formula; the theorems of Cauchy, Liouville, Morera, and Goursat; power series expansions; the Residue Theorem. Rouche's Theorem, the Schwartz Reflection Principle, and the Riemann Mapping Theorem." Prerequisite: MATH-236W and MATH-211. Offered in the spring semester of even years. Three hours per week. Four semester hours.
MATH-413. Numerical Analysis
Selected topics from numerical analysis, which may include systems of linear equations, linear and nonlinear differential equations, numerical integration and differentiation, eigenvalue problems, error analysis, interpolation and approximation. The computer will be used. This course will satisfy the college requirement for a capstone experience in the major. Prerequisite: MATH-211. Offered in the fall semester of even years. Three hours per week. Four semester hours. (R.)
MATH-421. Topology
Elementary point set topology; metric spaces; topological spaces, quotient spaces, compactness, connectedness, and applications of topology to digital graphics, sensor networks, and robotics. This course will satisfy the College requirement for a capstone experience in the major. Prerequisite: MATH- 236W. Offered in the spring semester of even years. Three hours per week. Four semester hours.
MATH-434. Number Theory
Divisibility; factorization; distribution of primes; modular arithmetic; Diophantine equations; theorems of Fermat, Euler and Wilson; primitive roots; public-key cryptography, quadratic reciprocity. Additional topics may include: applications to cryptography; digital signatures; algebraic and transcendental numbers; continued fractions; elliptic curves. This course will satisfy the College requirement for a capstone experience in the major. Prerequisite: MATH-236W. Offered in the fall semester of odd years. Three hours per week. Four semester hours.
MATH-442. Mathematical Statistics
The mathematical background of modern statistics, including the development of sampling distributions, the theory and application of estimation, tests of hypotheses. This course will satisfy the College requirement for a capstone experience in the major. Prerequisite: MATH-341. Offered in the spring semester. Three hours per week. Four semester hours.
MATH-451. Topics in Advanced Mathematics I
A course designed to acquaint the student with modern trends in advanced topics in mathematics and its applications. The course will be adapted to the students' preferences and needs. Prerequisite: Permission of the instructor. Three hours per week. Four semester hours. (R.)
MATH-452. Topics in Advanced Mathematics II
Independent research in mathematics. This course is appropriate for students pursuing departmental honors and distinguished honors projects, and is open to other students interested in research in mathematics. An oral presentation to the department is required. Prerequisites: Written consent of a member of the faculty to serve as an advisor. Four semester hours. (XLP.)
MATH-492W. Research/Independent Work
Independent research in mathematics. This course serves as the culminating course for departmental honors and distinguished honors projects. This course will satisfy the college requirement for a capstone experience in the major. Prerequisites: MATH-491, meets college and departmental requirements for honors, and written consent of a member of the faculty to serve as an advisor. Four semester hours. (XLP.)
STAT-140Q. Statistical Reasoning
A study of the role of statistics in a wide variety of academic fields and in everyday life. This course is intended for students who want an appreciation of statistics, but do not imagine that they will ever need to carry out statistical analyses themselves. Emphasis is placed on the ability to interpret and critically evaluate statistical claims. Offered both semesters. Three hours per week. Four semester hours (R.).
Note: This course cannot be counted toward a major or a minor in mathematics, a minor in statistics, or a minor in biostatistics. It is not a prerequisite for any other course. It cannot be taken for credit after or concurrently with any other statistics course, including AP Statistics.
STAT-141Q. Statistics I
A study of the fundamental concepts of statistical analysis. This course prepares students to carry out basic descriptive and inferential statistical analyses with the aid of computer software. Topics include an introduction to the nature of statistical reasoning, graphical and descriptive statistics, and design of experiments, sampling methods, probability, probability distributions, sampling distributions, and statistical inference based on confidence intervals and hypothesis tests. Examples will be drawn from a wide variety of disciplines. Offered both semesters. Four hours per week. Four semester hours. (R.)
Note: This course cannot be counted toward a major or a minor in mathematics. It cannot be taken for credit after or concurrently with any other statistics course, including AP Statistics.
STAT-240. Computational Statistics (SAS)
Statistical analysis using statistical software. Design, collection, organization, and storage of data sets. Statistical programming, debugging, analysis of output and interpretation of results. Prerequisite: MATH/STAT-141Q. Offered in the spring semester. Four hours per week. Four semester hours.
Note: STAT-240 does not fulfill the College Core Mathematics requirement.
STAT-242 Statistics II
A continued study of basic statistical techniques. Topics include: regression analysis, chi-square tests, nonparametric statistics, and the use of statistical software for data analysis. Prerequisite: STAT-141Q or MATH-442. Offered in the spring semester. Four hours per week.
STAT-243W Biostatistics
A study of inferential statistical techniques appropriate to the biological sciences. This course employs a case-study approach in which students use statistical software to examine real world data. Students will be required to produce statistical reports summarizing their statistical methods and results. Prerequisites: STAT-141Q or MATH-442. Offered in the fall semester. Four hours per week. Four semester hours. (R.)
Note: Students may not receive credit for both STAT-242 and STAT-243W.
STAT-342. Applied Regression Models
A study of regression models. This course will begin by considering the matrix approach to simple linear regression and progress to more general modeling approaches including multiple regression models and analysis of variance (ANOVA). Models, inferences, diagnostics, and remedial measures for dealing with invalid assumptions will be examined. Prerequisites: STAT-242 or 243W or MATH-235 or permission of instructor. Offered in the spring semester of even years. Three hours per week. Four semester hours.
STAT-382. Internship
An off-campus academic/work experience related to statistics conducted under the supervision of an internship adviser and an on-site supervisor. An oral presentation to the department is required. Contact the chair of the department for further details. Open to juniors and seniors. The term during which the internship work is performed will be noted by one of the following letters, to be added immediately after the internship course number: A (fall), B (winter), C (spring), or D (summer). Internships undertaken abroad will be so indicated by the letter I. The intern must complete a minimum of 160 hours of work. Graded S/U. Prerequisites: MATH/STAT-242 or 243(W), and approval of a faculty internship adviser. Four semester hours. (XLP.)
STAT-384. Internship in Biostatistics
STAT-392. Research/Independent Work
Independent investigation of an area of statistics not covered in regular courses. Prerequisite: Written consent of a department faculty member. Graded S/U. Two semester hours.
STAT-394. Independent Study
Independent investigation of an area of statistics not covered in regular courses. An oral presentation to the department is required. Prerequisite: Written consent of a department faculty member. Four semester hours. (XLP.)
STAT-441W. Applied Research Seminar in Biostatistics
A study of current problems in biostatistics. The course will introduce students to fundamental research procedures and data analysis. Students will work independently on a research problem of their choosing. Each student will be required to present on their progress throughout the semester and produce a culminating statistical report on their project. Students should expect to spend at least 12 hours per week working on their research project. Prerequisites: MATH/STAT-242 or MATH/STAT-243W and written permission of a department faculty member required. Four semester hours. (R.)
STAT-451. Topics in Advanced Statistics Faculty
A course designed to acquaint students with advanced topics in statistics and its applications. The course will be adapted to students' preference and needs. Prerequisite: Permission of the instructor. Three hours per week. Four semester hours. (R.)
Pfahler Hall 101


text:
\section{Methods}

{\bf Experimental conditions.}
Our system consists of $2 \times 10^4$ \K~atoms and $3.5 \times 10^5$ \Li~atoms confined in an optical dipole trap. The trap is realized with two crossed beams derived from a 1064\,nm single-mode laser source. The measured trap frequencies for Li (K) are $\nu_r = 690$\,Hz (425\,Hz) radially and $\nu_z = 86$\,Hz (52\,Hz) axially; this corresponds to a cigar-shaped sample with an aspect ratio of about 8. The preparation procedure is described in detail in Ref.~\cite{Spiegelhalder2010aop}. The Fermi energies, according to the common definition $E_F = h \sqrt[3]{6 N \nu_r^2 \nu_z}$ for harmonic traps, are $E_F^{\rm Li} = h \times 44\,{\rm kHz} = k_B \times 2.1\,\mu{\rm K}$ and $E_F^{\rm K} = h \times 10.4\,{\rm kHz} = k_B \times 500\,{\rm nK}$. At a temperature $T \approx 290$\,nK the \Li~component forms a deeply degenerate Fermi sea ($k_B T/E_F^{\rm Li} \approx 0.14$) while the \K~component is moderately degenerate ($k_B T/E_F^{\rm K} \approx 0.6$).

{\bf Effective Fermi energy.}
The \K atoms experience a nearly homogeneous \Li environment. This is because the optical trapping potential for \K~is about $2$ times deeper than for \Li and the \K~cloud is confined in the center of the much larger \Li Fermi sea \cite{Trenkwalder2011heo}. This allows us to describe the system in terms of the {effective Fermi energy} $\epsilon_F$, defined as the mean Fermi energy experienced by the \K atoms. We find $\epsilon_F = h \times 37\,$kHz, with two effects contributing to the fact that this value is about 15\% below $E_F^{\rm Li}$. The finite temperature reduces the Li density in the trap center, leading to a peak local Fermi energy of $h\times40$\,kHz. Moreover, the \K atoms sample a small region around the trap center, where the density and local Fermi energy are somewhat lower. The distribution of Fermi energies experienced by the \K cloud, i.e.\ the residual inhomogeneity of our system, can be quantified by a standard deviation of $h\times 1.9$\,kHz.

{\bf Concentration.}
The mean impurity concentration (mean density ratio $n_{\rm K}/n_{\rm Li}$) is about $0.4$, if one considers the population of K atoms in both spin states. This may be {\em a priori} too large to justify the interpretation of our data in terms of the low-concentration limit. We find that this interpretation is nevertheless valid, as we take advantage of several facts. Under strongly interacting conditions only a fraction of the K atoms is transferred into spin state $|1\rangle$ (see Fig.~2), which reduces the concentration of interacting impurities.
A recent quantum Monte Carlo calculation of the equation of state of a zero-temperature \Li-\K Fermi-Fermi mixture \cite{Gezerlis2009hlf} further supports our interpretation in the low-concentration limit: The strongest interaction in the mass-imbalanced system is expected when one has about 4 times more \K atoms than \Li atoms, and for concentrations up to a value of 1 the interaction energy per \K atom is expected to remain essentially constant. To support our basic assumption with experimental data, we also took rf spectra for variable numbers of \K atoms, confirming that in the relevant parameter range finite concentration effects remained negligibly small.

{\bf Interaction control via Feshbach resonance.}
The Feshbach resonance used for interaction tuning is discussed in detail in Refs.~\cite{Naik2011fri, Trenkwalder2011heo}. It is present for \Li in the lowest spin state and \K in the third-to-lowest spin state. The latter represents our interacting state $|1\rangle$; the corresponding quantum numbers are $F=9/2$ for the hyperfine and $m_F=-5/2$ for the magnetic sub-state. The neighboring state with $m_F=-7/2$ serves as state $|0\rangle$; here the interspecies scattering length (about $+65\,a_0$ with $a_0$ being Bohr's radius) is so small that it can be neglected to a good approximation. The tunable scattering length for state $|1\rangle$ in the Fermi sea is well described by the standard formula $a = a_{\rm bg} (1-\Delta B/(B-B_0))$ with $a_{\rm bg} = 63.0\,a_0$, $\Delta B = 880\,$mG, and $B_0 = 154.719(2)\,$G. Note that the value given for $B_0$ refers to the particular optical trap used in the experiments, as it includes a small shift induced by the trapping light. The value therefore somewhat deviates from the one given in Refs.~\cite{Naik2011fri, Trenkwalder2011heo}. In free space, without the light shift, the resonance center is located at 154.698(5)\,G.
The character of the resonance is closed-channel dominated \cite{Chin2010fri}. Following the definition \cite{Petrov2004tbp} of a range parameter $R^* = \hbar^2/(2 m_r a_{\rm bg} \, \delta \mu \, \Delta B)$, with $m_r = m_{\rm Li}m_{\rm K}/(m_{\rm Li} +  m_{\rm K})$ being the reduced mass and $\delta \mu$ the differential magnetic moment, the resonance is characterized by $R^* = 2700\,a_0$. This value accidentally lies very close to $1/\kappa_F = 2850\,a_0$, which also means that the strongly interacting regime roughly corresponds to the universal range of the resonance. Our system therefore represents an intermediate case ($\kappa_F R^* = 0.95$), where the behavior is near universal, but with significant effects arising from closed-channel contributions.

{\bf Details on Rf pulses.}
For taking the data of Fig.~2 we used Blackman pulses \cite{Kasevich1992lcb} to avoid side lobes in the spectrum. For the upper panel, the pulses were 1\,ms long (spectral width $0.7\,{\rm kHz} \simeq 0.02\,\epsilon_F/h$) and the rf power was adjusted such that $\pi$-pulses would be realized in the absence of interactions with the Fermi sea. For the data in the lower panel, the rf power was increased by a factor of 100 and the pulse duration was set to 0.5\,ms. This resulted in pulses with an area of 5$\pi$ without the Fermi sea.
For the lifetime measurements in Fig.~3, we used a sequence of 3 Blackman pulses. The first pulse (duration between $150\,\mu$s and $500\,\mu$s) was set to drive the non-interacting impurity from spin state $|0\rangle$ ($m_F=-7/2$) into state $|1\rangle$ ($m_F=-5/2$); here the frequency was carefully set to resonantly create repulsive polarons and the pulse area was set to fulfill the $\pi$-pulse condition. The second pulse was a short ($60\,\mu$s) cleaning pulse, which removed the population remaining in $|0\rangle$ by transfer to another, empty spin state ($m_F=-9/2$). The third pulse had the same parameters as the first one and resonantly back-transferred the population from the polaronic state in $|1\rangle$ to the non-interacting state $|0\rangle$, where it was finally measured by spin-state selective absorption imaging.
The measurements of Rabi oscillations in Fig.~4 were performed with simple square pulses.

\section{Supplementary Information}

\subsection{1. Theoretical framework}
\label{theoryIntro}

The theoretical results presented in the main text and in this Supplementary Information are obtained from a model that describes the behaviour of a single impurity embedded in a Fermi sea with tuneable $s$-wave interaction near a Feshbach resonance with arbitrary effective range. Two different wavefunctions are needed, depending on whether one is interested in the polaron \cite{Chevy2006upd,Combescot2007nso} or molecule \cite{Mora2009gso,Punk2009ptm,Combescot2009ato} properties. The quasiparticle parameters
for the polaron (energy $E_+$ and $E_-$, residue $Z$, effective mass) and the molecule properties can be found either variationally, or diagrammatically using the ladder approximation. Both approaches yield identical results, which closely match independent Monte-Carlo calculations \cite{Prokofev2008fpp}. The properties of the repulsive polaron, which is intrinsically unstable due to the presence of the molecule-hole continuum (MHC) and of the attractive polaron, are obtained from the self energy. In particular, the interaction induced energy shift and the decay rate are given by the real part and twice the imaginary part of the self energy, respectively \cite{Massignan2011rpa}.

Previous treatments \cite{Chevy2006upd,Combescot2007nso,Mora2009gso,Punk2009ptm,Combescot2009ato,Prokofev2008fpp,Massignan2011rpa} were based on a universal scattering amplitude, describing broad Feshbach resonances. To include effects of the finite effective range we employ a many-body T-matrix given by \cite{Bruun2005msa, Massignan2008esn}
\begin{equation}
T({\bf K},\omega)=\left[\frac{m_{r}}{2 \pi \hbar^2 \tilde{a}({\bf K},\omega)}-\Pi({\bf K},\omega)\right]^{-1}.
\label{T_mu_abg}
\end{equation}
Here $\hbar {\bf K}={\bf p}_{\rm K}+{\bf p}_{\rm Li}$ is the total momentum with ${\bf p}_{\rm Li}$ and ${\bf p}_{\rm K}$ the momenta of \Li and \K, $m_r=m_{\rm Li} m_{\rm K}/(m_{\rm Li}+m_{\rm K})$ the reduced mass, $\Pi(K,\omega)$ the \Li-\K pair propagator in the presence of the Fermi sea, and $\tilde a({\bf K},\omega)\equiv a_{\rm bg}\left(1-\frac{\Delta B}{B-B_0-E_{\rm CM}/\delta\mu}\right)$ an energy-dependent length parameter, with $a_{\rm bg}$, $\Delta B$, $B_0$, and $\delta\mu$ being the background scattering length, the width, the center, and the relative magnetic moment of the Feshbach resonance. $E_{\rm CM}({\bf K},\omega)=\hbar\omega-\hbar^2{\bf K}^2/(2M)+\epsilon_F$, with $M=m_{\rm Li}+m_{\rm K}$, is the energy in the center of mass reference frame of the colliding pair. In vacuum and close to resonance, the scattering amplitude of our model has the usual low energy expansion
\begin{equation}
-f_k^{-1}=a^{-1}+ik-r_{e} k^2/2+\ldots,
\label{equ_expansion}
\end{equation}
with the relative momentum $\hbar {\bf k}=(m_{\rm Li}{\bf p}_{\rm K}-m_{\rm K}{\bf p}_{\rm Li})/M$. The effective range is approximated by $r_{e}\approx-2R^*(1-a_{\rm bg}/a)^2$, where we introduce the range parameter $R^\ast=\hbar^2/(2m_r a_{\rm bg}\Delta B \delta\mu)$, see Ref.~\cite{Petrov2004tbp}. A detailed theoretical analysis of this model will be given elsewhere \cite{Massignan2011ppp}.

\subsection{2. Polaron peak in the spectral response}
\label{sec_peak}

\begin{figure} [!h]
\begin{center}
\hspace{+75pt}\includegraphics[width=8cm]{figS1a}
\includegraphics[width=7cm]{figS1bcd}
\caption{Double Gauss analysis of the low-power spectra. The data are the same as presented in Fig.~2a plus additional data in an extended range of $1/(\kappa_F a)$. (a) The Gauss function fitting the wide background is shaded grey. The Fourier-limited Gauss function, fitting the narrow peak, is coloured red (green) along the repulsive (attractive) polaron branch. We identify the narrow peak with one of the polaron branches only if its maximum signal exceeds a threshold value of 0.085, corresponding to two times the standard deviation of the noise in our data. Any smaller peak may be caused by fitting to a noise component. The lower panels show (b) the maximum signal of the narrow peak with the dashed line indicating the threshold, (c) the area under the wide Gauss function normalized to its maximum value, and (d) the detuning at the center of the narrow peak, provided that the peak signal exceeds the threshold, compared to the theoretical calculation of $E_+$ and $E_-$ (red and green line). The error bars indicate the fit uncertainties.} \label{fig_peak} \end{center} \end{figure}

The spectra in Fig.~2a of the main text show a narrow, {\it coherent} peak on top of a spectrally broad, {\it incoherent} background. Here, we investigate these two spectral parts in more detail. Note that the background is actually better visible in Fig.~2b, but these spectra do not allow for a quantitative comparison of the two parts because of the strong saturation of the narrow polaron peaks.

The narrow peak stems from the attractive or repulsive polarons, which correspond to well defined energy levels, provided that the lifetime of the quasiparticle exceeds the pulse duration. As a consequence, the lineshape is expected to be Fourier limited except for the rapidly decaying repulsive polarons very close to resonance. In contrast, the background is spectrally wide, on the order of $\varepsilon_F$. The main contribution to the background stems from the MHC. Another contribution may arise from the excitation of additional particle-hole pairs in the Fermi sea when transferring to a quasiparticle with a momentum that is different from the momentum of the impurity in the initial state.

We distinguish between the narrow peak and the wide background by means of a double Gauss fit. Vertical cuts through Fig.~2a are presented in Fig.~\ref{fig_peak}a together with the fit curves. The width $\sigma_p$ of the Gauss function fitting the narrow peak is fixed to the one associated with the Gaussian fit of the Blackman pulse line shape used in the experiment, $\sigma_p=0.7\,$kHz$=0.019\,\varepsilon_F/h$. We constrain the width $\sigma_b$ of the Gauss function reproducing the background to $3\times0.019\,\varepsilon_F/h<\sigma_b<0.5\,\varepsilon_F/h$. The lower bound avoids the misinterpretation of the narrow peak as background and the upper bound, corresponding to the maximal width of the continuum as obtained from the spectra in Fig.~2b, avoids unphysically large values of $\sigma_b$ when the background signal is weak. We find that the narrow peak dominates for weak positive and negative interaction strength while the wide background dominates in the strongly interacting regime. This trend is shown in Fig.~\ref{fig_peak}b and Fig.~\ref{fig_peak}c, where we present the maximum signal of the narrow peak and the area of the background, respectively. Note, that the signal in Fig.~\ref{fig_peak}b is proportional to the area of the narrow peak since $\sigma_p$ is kept constant. Figure \ref{fig_peak}d shows the detuning at the center of the narrow peak, which corresponds to the energy of the quasiparticles. The measured energies agree remarkably well with the calculation. The slight mismatch between theory and experiment may be attributed to systematic errors in the determination of $\varepsilon_F$ and $B_0$.

The area of the wide background exhibits a maximum close to $-1/(\kappa_Fa)=\,0$, but it shows an asymmetry as it falls off significantly slower on the attractive ($a<0$) side, see Fig.~\ref{fig_peak}c. We attribute this asymmetry to the narrow character of the Feshbach resonance. The interaction becomes resonant when the real part of the inverse scattering amplitude, given in Eq.~\ref{equ_expansion}, is zero. This leads to the resonance condition $a_{\rm res}^{-1}=r_{e} k^2/2$, where $a_{\rm res}$ is the value of the scattering length at which the interaction becomes resonant. In the limit of a broad resonance with $r_{e}=0$, this condition is fulfilled for any $k$ at the center of the resonance, where the scattering length diverges. However, at a narrow resonance with $r_{e}<0$ the condition requires a negative $a_{\rm res}$ for $k>0$. The mean square momentum in the Fermi sea is $3/5\times\kappa_F^2$, leading to a mean square relative momentum of $3/5\times(40/46\times\kappa_F)^2$. Using this value for $k^2$, and inserting $r_e\approx-2R^\ast$
in the above resonance condition, we obtain $-1/(\kappa_Fa)=\,0.43$. This represents an effective shift of the Feshbach resonance center, as we average over all momenta of the Fermi sea \cite{Ho2011aro}. The magnitude of this shift agrees well with the observed asymmetry. Moreover, we find that many features at our narrow resonance appear to be shifted, e.g.~the polaron-to-molecule crossing. However, the narrowness has many more implications and cannot simply be reduced to this shift. We will come back to this point in the context of the lifetime of the repulsive polaron, see Sec.~4.

The repulsive polaron peak is clearly visible up to $-1/(\kappa_F a)\approx-0.3$ while the attractive polaron peak vanishes already at $-1/(\kappa_F a)\approx0.9$, see Fig.~\ref{fig_peak}b. The fading out of the quasiparticle peak towards the strongly interacting regime approximately coincides with the position where the quasiparticle branches merge into the MHC. This shows that the polaron state is hardly observable as soon as it becomes degenerate with molecule-hole excitations. The MHC is not strictly limited to the range from $E_m$ to $E_m-\varepsilon_F$, as discussed in more detail in Sec.~3. It extends below $E_m-\varepsilon_F$ because of finite temperature effects. It also extends slightly above $E_m$ because of additional excitations in the spectral function of the molecules \cite{Schmidt2011esa}. As a consequence, for finite temperature, the attractive polaron can become degenerate with molecule-hole excitations for values of the interaction parameter above the calculated polaron-to-molecule crossing. This explains that the observed sharp peak is observed to disappear already at $-1/(\kappa_Fa)\approx0.9$, which lies somewhat above the zero-temperature polaron-to-molecule crossing predicted at $0.6$.

It is interesting to consider the data analysis presented in Fig.~\ref{fig_peak}b and c in relation to the common method of extracting the quasiparticle residue $Z$ from the spectral weight of the narrow peak \cite{Ding2001cqw}. Close to resonance, we are in the linear response regime and our data can be interpreted in terms of this method. Our data suggests that this method leads to a significant underestimation of $Z$. For example at $-1/(\kappa_F a)\approx0.9$, where the narrow peak of the attractive polaron vanishes, our theory still predicts $Z\approx0.7$. This underestimation is consistent with the one reported in Ref.~\cite{Schirotzek2009oof}, see also related discussion in Ref.~\cite{Punk2009ptm}. A plausible explanation may be that such a method does not probe the polaron states alone, but also the molecule-hole excitations, which are degenerate with the polaron state. Our alternative method of measuring the residue via the Rabi frequency, as presented in the main paper, offers the advantage of being much less affected by the molecule-hole contribution. In fact, only the coherent part of the quasiparticle is expected to produce Rabi oscillations, see Sec.~6.

\subsection{3. Molecule-hole continuum}
\label{sec_MHC}

The spectra presented in Fig.~2b of the main text reveal the MHC. This continuum arises from processes where the rf field associates a \K impurity and a \Li atom out of the Fermi sea to a molecule. Here we present a simple model for the spectral line shape, which allows us to interpret the data up to $-1/(\kappa_F a)\approx-1$, see Fig.~\ref{fig_MHC}.

\begin{figure} [h]
\begin{center}
\includegraphics[width=8cm]{figS2}
\caption{Molecule association spectra for different values of the interaction parameter. The signal is the fraction of transferred atoms as a  function of the rf detuning. The data correspond to vertical cuts through Fig.~2b. The dashed line is the line shape model for zero temperature and the solid line for finite temperature. The upper threshold of the theoretical spectra corresponds to $E_m$.}
\label{fig_MHC} \end{center} \end{figure}

For modeling the line shape, we consider two-body processes in which the rf field associates one \K and one \Li atom to a molecule. Higher-order processes, involving more than two particles, are neglected in this model but are briefly discussed at the end of this section.  Let us first consider the association of \Li and \K with momenta $p_{\rm Li}=p_{\rm K}=0$. This results in a molecule at rest plus a Fermi sea with a hole in the center. The energy of this state is determined by the binding energy of the molecule and by the interaction of the molecule with the Fermi sea. It is given by $E_m$ and sets the onset of the MHC from the right (the top) in Fig.~\ref{fig_MHC} (Fig.~2b). In general, \Li and \K have finite initial relative momentum $\hbar k$, leading to an initial relative kinetic energy in the center of mass frame $E_r=\hbar^2k^2/2 m_r$. The energy conservation of the association process is expressed in the Dirac $\delta$ function in Eq.~\ref{equ_mhc}. As a consequence, the molecule spectrum extends downwards to energies below $E_m$. We now consider an ensemble of \K and \Li atoms. Our experimental conditions are well approximated by a thermal cloud of \K in a homogeneous Fermi sea of \Li (see Methods). The momentum distribution of \Li is given by the Fermi-Dirac distribution $f^{\rm FD}_{\rm Li}(E_{\rm Li})$, with $E_{\rm Li}=p_{\rm Li}^2/2m_{\rm Li}$. The one of \K is approximated by the Maxwell-Boltzmann distribution $f^{\rm MB}_{\rm K}(E_{\rm K})$, with $E_{\rm K}=p_{\rm K}^2/2m_{\rm K}$. The latter distribution does not change its momentum dependence with position, thus, no integration over space is needed to obtain the spectral response
\begin{equation}
\label{equ_mhc}
\begin{split}
\mathcal{S}(\Delta)\propto \int\int d^3p_{\rm Li} ~~d^3p_{\rm K}
~~f^{\rm FD}_{\rm Li}(E_{\rm Li}) \\ ~~f^{\rm MB}_{\rm K}(E_{\rm K}) ~~\mathcal{F}(k) ~~\delta(-E_m+E_r+\Delta),
\end{split}
\end{equation}
where $\mathcal{F}(k)$ is the Franck Condon overlap of the initial wavefunction with the molecule wavefunction. In our case the interaction in the initial state is negligible and $\mathcal{F}(k)$, as given in Ref.~\cite{Chin2005rft}, reduces to $\mathcal{F}(k)\propto (E_r/E_b^3)^{1/2}(1+E_r/E_b)^{-2}$. The parameter $E_b$ is the binding energy of a molecule in vacuum at a resonance with finite effective range and reads $E_b=\hbar^2/(2 m_r a^{\ast2}) $ with the parameter \cite{Petrov2004tbp} $a^\ast=-r_e/(\sqrt{1-2r_{e}/a}-1)$. In the calculation of $\mathcal{F}(k)$, we do not account for interactions with the Fermi sea. Because of this approximation, we apply the model only for $-1/(\kappa_F a)<-1$. For fitting the model line shapes to the experimental data, adjustable parameters are the individual heights of the spectra and the center of the Feshbach resonance. The latter parameter is required to be the same for all data sets in Fig.~\ref{fig_MHC}. Independently determined parameters are $k_B T/\varepsilon_F=0.16$ and $\varepsilon_F=h\times 37$\,kHz. The model (solid lines) reproduces our data remarkably well. It allows us to pinpoint the resonance position to $B_0 = 154.719(2)\,$G. This determination of $B_0$ relies on our theoretical model to calculate $E_m$. To test this model dependence, we replace $E_m$ simply by the binding energy of the molecule in vacuum plus the mean field energy, considering the corresponding atom-dimer scattering length \cite{Levinsen2011ada}. Using this simple model, the fit yields a resonance position that is 1\,mG higher, which shows that the model dependence causes only a small systematic uncertainty. Moreover, the statistical fit uncertainty and the field calibration uncertainty are about 1\,mG each.

For $T=0$ and all other parameters unchanged, the model provides the dashed lines in Fig.~\ref{fig_MHC}. The spectra show a sharp drop at $\Delta=E_m-(40/46)\,\varepsilon_F$, which corresponds to the association of an impurity at rest and a majority atom at the Fermi edge.
In an equal-mass mixture this process would occur at $\Delta=E_m-(1/2)\,\varepsilon_F$. Thus, the width of the MHC in the two-body approximation is much larger for a heavy impurity than it is for an equal-mass impurity and it is even narrower for a light impurity.

The true zero temperature ground state is actually at the energy $E_m-\varepsilon_F$, a molecule at rest formed from a \K atom at rest and a \Li atom at the Fermi edge. However, to reach this state, momentum conservation requires a higher-order process, i.e.~the scattering of at least one additional \Li atom from and to the Fermi surface. Such processes are not included in the model presented here, which only considers the direct association of two atoms by an rf photon.

In the strongly interacting regime the spectral function of the molecule shows additional excitations above the molecular ground state \cite{Schmidt2011esa}. This leads to an extension of the MHC spectral response above $E_m$, of which we find clear indications in our data. The lower panel in Fig.~\ref{fig_MHC} shows finite signal above $E_m$ and the extension above $E_m$ is very evident in the strongly interacting regime, see Fig.~2b.

\subsection{4. Decay rate of the repulsive polarons}
\label{sec_decayrate}

We analyse the decay of the repulsive polarons by assuming that they decay into well defined attractive polarons or well-defined molecules.
In this  quasiparticle picture, the decay is associated with the formation of a particle-hole pair in the Fermi sea to take up the released energy. In this sense,
the decay into the attractive polaron is a 2-body process and the decay into the molecule is a 3-body process. We calculate the decay rate for these two channels by including them into the polaron self energy using a pole expansion of the \K propagator writing $G({\mathbf k},\omega)\simeq Z_+/(\hbar\omega-E_+-\hbar^2k^2/(2m_{\rm K}))+Z_-/(\hbar\omega-E_--\hbar^2k^2/(2m_{\rm K}))$ and
a pole expansion of the T-matrix writing $T({\mathbf k},\omega)\simeq Z_mg^2/(\hbar\omega-(E_m-\varepsilon_F)-\hbar^2k^2/(2M))$. Here,  $Z_{\pm}$ is the quasiparticle residue of the repulsive and attractive polaron respectively and $Z_m$ the quasiparticle residue of the molecule. The factor $g^2=2\pi\hbar^4 /(m_r^2a^\ast\sqrt{1-2r_{e}/a})$ is the residue of the vacuum T-matrix for a general resonance. The details of this approach are given in Refs.~\cite{Massignan2011rpa,Bruun2010dop}, the only difference being that here we include the effects of the finite effective range. The imaginary part of the self energy gives the decay rate of the wavefunction and we thus take twice the imaginary part to calculate the population decay. The 2-body decay into the attractive polaron and an additional particle-hole pair
is calculated numerically to all orders in the T-matrix by inserting the pole expansion for the \K propagator in the self energy in the ladder approximation. For the 3-body decay  into a molecule and an additional particle-hole pair, we include terms containing two \Li holes in the \K self energy \cite{Bruun2010dop}, and an expansion to second order in the T-matrix relevant for $-1/(\kappa_Fa)\ll-1$ yields
\begin{equation}
\begin{split}
\Gamma_{PM}\simeq\frac{64\kappa_Fa}{45\pi^3}\frac{Z_{+}^3}{m_{\rm K}^2\sqrt{m_{\rm Li}}}\left(1+\frac{m_{\rm Li}}{M}\right)^{3/2}\\ \left(\frac{\hbar\kappa_F}{\sqrt{2(E_+-E_m+\epsilon_F)}}\right)^{5}
\frac{a}{a^\ast\sqrt{1-2r_{e}/a^\ast}}\frac{\epsilon_F}{\hbar}.
\end{split}
\label{3bodyDecay}
\end{equation}
For simplicity, we have taken $Z_m=1$, which is an appropriate assumption for $-1/(\kappa_Fa)\ll-1$. The effect of the narrow resonance on the decay rate enters through the quasiparticle residue $Z_+$, the energies $E_+$, $E_-$, $E_m$ and directly through the effective range $r_{e}$. This decay rate has the same $a^6$ dependence as the three-body decay in vacuum in the limit of a broad resonance derived in Ref.~\cite{Petrov2003tbp}. The numerical prefactor however differs since we have included the effects of the Fermi sea in a perturbative calculation.

\begin{figure} [t]
\begin{center}
\includegraphics[width=8cm]{FigS4}
\caption{Decay rates of repulsive \K polarons in a Fermi sea of \Li atoms, shown as a function of interaction strength (left) and of the energy of the repulsive polaron (right). Blue and red lines represent the two- and three-body contributions, respectively, while data points are the experimental findings as also shown in Fig.~3 of the main text. The results for the moderately narrow resonance under study here (solid lines) is compared with the theoretical results obtained for the universal limit of a very broad resonance (dashed lines). The experimental values of $E_+$ are obtained by interpolation of the narrow peak position data $\Delta_{\rm peak}$, see Fig.~\ref{fig_peak}d.}
\label{fig_comparedecay} \end{center} \end{figure}

The results for the decay rates of repulsive polarons are shown in Fig.~\ref{fig_comparedecay}. The experimental data agree well with the theoretical results obtained for our narrow resonance (continuous lines) as already shown in Fig.~3 in the main text. For comparison, we also show the decay rates one would obtain in the limit of a broad resonance (dashed lines). We find that as magnitude of the effective range increases with respect to the interparticle spacing, the dominant two-body decay is strongly suppressed. This suppression is mainly due to a large reduction of the attractive polaron residue $Z_{-}$. Instead, the weaker three-body decay increases, which we attribute to the reduction of the polaron-molecule energy difference $E_+-E_m+\epsilon_F$. Taking both decay rates together, the decay rate is at least an order of magnitude smaller at our narrow resonance as compared to the case of a broad resonance. It is important to note that this strong suppression of the decay at a given $-1/(\kappa_Fa)$ cannot be simply attributed to the effective resonance shift at our narrow Feshbach resonance as discussed in Sec.~2. When taking this shift into account, a suppression factor of five to ten remains. To highlight this point, we choose a representation that is independent of the interaction parameter and that gives the dependence on the polaron energy, a direct manifestation of strong interactions. The right panel shows the same data and calculations as a function of $E_+$. Also for a given $E_+$, the repulsive polaron at our narrow resonance turns out to be much more stable than the repulsive polaron at a broad resonance.

\subsection{5. Decay of repulsive polarons to molecules}

The decay of the repulsive polarons, shown in Fig.~3 of the main text, is measured by applying a special three-pulse scheme (see Methods). In this section we exploit the flexibility of this scheme to study the decay to lower-lying energy states in more detail. At a given interaction strength $-1/(\kappa_F a)=-0.9$, we demonstrate that the repulsive polarons decay to molecules by showing that an rf spectrum taken after decay perfectly matches a reference spectrum of molecules.

To populate the repulsive polaron branch, as done for the measurements of the decay rate, we tune the energy of the first pulse to $E_+$, corresponding to $\Delta=0.16\,\varepsilon_F$ at $-1/(\kappa_F a)=-0.9$. The pulse duration ($t_p=0.06\,$ms) and the intensity are set to correspond to a $\pi$-pulse in the noninteracting system. The second pulse removes the remaining non-transferred atoms by transferring them to a third spin state. In contrast to the decay measurement presented in the main text, we here use much more rf power for the third pulse to be able to efficiently dissociate molecules. For this purpose, we set $t_p=0.3\,$ms and the pulse area corresponds to a $3\pi$-pulse in the noninteracting system. By varying the rf detuning, we record spectra for zero hold time (black squares) and for a hold time of $2\,$ms (red dots), see Fig.~\ref{fig_decayproducts}a. The peak at small positive detuning shows the back-transfer of repulsive polarons. The corresponding signal decreases with hold time, signalling the decay of the repulsive polaron. In addition, a wide continuum in a range of negative detunings rises with increasing hold time. Such a wide continuum involves coupling to high momentum states, signaling a short distance between \K and $^6$Li. To confirm that this continuum stems from molecules, we compare it to a reference spectrum of the dissociation of molecules (blue diamonds). We find a perfect match. To take such a reference spectrum, only the detuning of the first rf pulse is changed to directly associate molecules in the MHC instead of populating the repulsive polaron branch. We achieve a good association efficiency with $\Delta=-0.54\,\varepsilon_F$ and $t_p=0.5\,$ms.

\begin{figure} [h]
\begin{center}
\includegraphics[width=6cm]{figS3a}
\includegraphics[width=6cm]{figS3b}
\caption{Decay of repulsive polarons to molecules at $-1/(\kappa_F a)=-0.9$. (a) The black squares (red dots) show the spectrum right after ($2\,$ms after) the repulsive polaron has been populated. The blue diamonds show the dissociation spectrum of molecules for reference. The signal is the fraction of atoms transferred from the interacting spin state \ket{1} to the noninteracting spin state \ket{0}. Note that the polaron peak at positive detuning is highly saturated and thus its signal is not proportional to the number of polarons. (b) The rf energy detuning is fixed to $\Delta=-1.3\,\varepsilon_F$ and the signal is recorded versus hold time. The error bars indicate the statistical uncertainties derived from at least three individual measurements.}
\label{fig_decayproducts}
\end{center}
\end{figure}

To study the evolution of the molecule population, which is fed by the decay of the repulsive polarons, we set the detuning of the third pulse to the peak of the molecule signal at $\Delta=-1.3\,\varepsilon_F$ and record the signal as a function of the hold time, see Fig.~\ref{fig_decayproducts}b. A simple exponential fit yields a rate of about 1\,ms$^{-1}$=\,0.0043\,$\varepsilon_F/\hbar$, which is in good agreement with the measured decay rate of the repulsive polaron at $-1/(\kappa_F a)=-0.9$. The finite signal at zero hold time may have two origins. One contribution is some decay during the finite pulse durations of the three pulses, which are not included in the hold time. Another contribution may be the high momentum tail of the repulsive polarons as discussed in Ref.~\cite{Schirotzek2009oof}.

Note that we do not find any second sharp peak at negative detuning, which would indicate the population of the attractive polaron branch. In case the repulsive polaron decays to the attractive polaron, the absence of the attractive polaron peak implies a very rapid subsequent decay of the attractive polaron to the MHC. Such a fast decay of the attractive polaron to the MHC is consistent with the very small signal of the attractive polaron peak throughout the regime of strong interaction as discussed in Sec.~2.

Let us briefly discuss the possible role of inelastic two-body relaxation in the \Li-\K mixture, which is energetically possible as \K is not in the lowest spin state. This process was identified in Ref.~\cite{Naik2011fri} as a source of losses.
However, this relaxation is about an order of magnitude slower than the measured decay rate of the repulsive polaron and thus does not affect our measurements.

\subsection{6. Rabi oscillations and polaron quasiparticle residue}
\label{sec_Z}

For high rf power, the signal is well beyond linear response and the \K atoms  exhibit coherent Rabi oscillations between the spin states \ket{0} and \ket{1}. In this regime the oscillations are so fast, that the polaron decay plays a minor role and can be ignored to a first approximation. The Rabi frequency depends on the matrix element of the rf probe between the initial state \ket{0} and the final state \ket{1}. Since the probe is homogenous in space, it does not change the spatial part of the atomic wavefunction and it can be described by the operator \cite{Massignan2008tpi} $\hat R \propto \Omega_0\sum_{\bf q}(\hat a_{1\bf q}^\dagger\hat a_{0\bf q}+h.c.)$ where $\hat a^\dagger_{i{\bf q}}$ ($\hat a_{i{\bf q}}$) creates (annihilates) a \K atom with momentum ${\bf q}$ in spin state $i$ and $\Omega_0$ is the unperturbed Rabi frequency of the $|0\rangle$ to $|1\rangle$ transition in the non-interacting case. Considering for simplicity an impurity at rest, the initial non-interacting state is given by $|I\rangle=\hat a_{0{\bf q}=0}^\dagger|{\rm FS}\rangle$ where $|{\rm FS}\rangle$ is the \Li Fermi sea. The final polaronic state at zero momentum can be written as \cite{Chevy2006upd}
\begin{equation}
|F\rangle= \sqrt{Z} \hat a_{1{\bf q}=0}^\dagger|{\rm FS}\rangle +
\sum_{q<\hbar\kappa_F<p}\phi_{{\bf p},{\bf q}} \hat a_{1{\mathbf q}-{\mathbf p}}^\dagger
\hat b^{\dag}_{{\bf p}}\,\hat b_{{\bf q}}|{\rm FS}\rangle+\ldots
\label{ansatz}
\end{equation}
where $\hat b^\dagger_{\bf q}$ ($\hat b_{\bf q}$) creates (annihilates) a \Li atom with momentum ${\bf q}$. The second term contains a Fermi sea with at least
one particle-hole excitation and thus is orthogonal to an unperturbed Fermi sea. Therefore the  matrix element reduces to $\langle F|\hat R|I\rangle=\sqrt{Z}\,\Omega_0$ and we obtain the Rabi frequency
\begin{equation}
\Omega=\sqrt{Z}\,\Omega_0.
\end{equation}
We neglect the momentum dependence of the quasiparticle residue and do not perform a thermal average over the initial states, which we expect to be a good approximation
since $T\ll \epsilon_F/k_B$.

\begin{figure} [t]
\begin{center}
\includegraphics[width=8cm]{FigS5}
\caption{Linear increase of the Rabi frequency $\Omega$ with the unperturbed Rabi frequency $\Omega_0$. The left (right) panel shows the driving to the repulsive (attractive) polaron. The solid lines are linear fits without offset and demonstrate the proportionality $\Omega\propto\Omega_0$.} \label{fig_omega} \end{center} \end{figure}

In Fig.~\ref{fig_omega} we plot the observed Rabi frequency $\Omega$ as a function of the unperturbed Rabi frequency $\Omega_0$. We find that the proportionality $\Omega\propto \Omega_0$ holds over a wide range of rf power. The measurements presented in the main text, taken at $\Omega_0=2\pi\times 6.5\,$kHz and 12.6\,kHz, are safely within this range.

\bibliographystyle{apsrev}

redpajama_set_name: RedPajamaArXiv


Here you bring your enthusiasm for life and an open schedule.
The pioneer spirit of Robson Ranch Texas means plenty of room to explore favorite interests and new hobbies. You'll enjoy meeting friends who share your enthusiasm for events like the popular softball games, musicals and concerts in the ballroom, and happy hour at the dog park.
Games are played to 15 points with rally-style scoring. The Club referees their own games so fundamentals are important, but they have a lot of folks that carry the ball, or fall on the net, so it is mainly fun and a very good activity.
The Robson Ranch Softball Association wishes to invite any and all residents to their league for the fun and sport of playing softball on the beautiful field. The co-ed league is rapidly growing and welcomes new participants.
The Robson Ranch Tennis Club was founded to encourage tennis players of all levels to play tennis, have fun and remain active.
All residents are invited to join the pickleball program at Robson Ranch. Pickleball is a fun, fantastic exercise program that will improve your lifestyle, your health and the enjoyment of your senior years.
Weather permitting; the Robson Ranch Women's Golf Association (RRWGA) has a weekly Ladies' Play Day. The association's objective is to compete and have fun on the golf course.
Come join this club for singles and doubles table tennis in the gym.
Watch our Weight (WOW) is a weight-loss and maintenance support group. The group is made-up of friendly folks from around Robson Ranch looking for helpful suggestions and reminders to keep their weight within a healthy range. For more information, stop by one of their meetings to sample their fun and supportive group.
Warm up exercises, aerobic exercises, barbell exercises with aerobics, noodle exercises and cool down stretches with deep breathing.
This basketball club encourages men, who still like to play this game, to join the fun. They have 4 on 4 games when possible but are in need of more players. Plus, they play half court and to 11 with a regular basket counting 1-point and a (normal) 3-point shot counting at 2 points. All games are played for fun, as they do not want anyone to incur an injury. After they have played enough games where most of the players are tuckered out, they often close out with some team shooting games. Come and join them if you still have some "game" or want to try to re-establish the "game" that you once had.
Robson Ranch has numerous performance art clubs, including ballroom dance classes, community choir, music club and country western dance.
Country Western Line, Partners, and Couples' lessons are given on the dance floor at the Robson Ranch Clubhouse. Country Western dancing is great exercise for your body and even better exercise for your brain! The basic goal is for you to get out on the dance floor, have a good time and meet some great people.
Come join the fun and take a Ballroom Dance Class.
The Robson Ranch Dance Club sponsors four dances each year: The Valentine Dance in February, Spring Fling Dance in April, Summer Celebration Dance in July, and The Fall Harvest Dance in October. Each seasonal dance features a different dance lesson and will be advertised when tickets go on sale.
Music Club includes the Community Choir, made up of over 70 men and women, all Robson Ranch residents. The choir produces three professional concerts a year at the Main Clubhouse. They sponsor other events, including multiple Karaoke and Dance Nights, Fourth of July Band Night, and other musical entertainment. The choir meets every Monday night, for concert rehearsals, from September until April. They break for summer.
If you would like to play in the clay, then join the group of Happy Potters. Explore your creative side and see what you can make from a bag of clay on the pottery wheel or the slab roller.
Members create beautiful works of art as well as useful home and garden items. They have over 800 molds for members to pour and 3 kilns to fire their creations. New members will be taught how to pour and painting techniques. You will need to allow 3 to 4 hours minimum to pour molds. A normal annual user fee is charged to pay for supplies, as well as a very small pouring and firing fee. Come join the fun!
This group encourages residents and guests to bring their current scrapbooking project and to work on it alongside other scrapbookers. For those who are new to scrapbooking or who need assistance in planning and carrying out a project, assistance is provided. From time to time, they provide instructional activities, announcing them in advance to all Robson Ranch residents. There are no dues, nor reservations required.
The Woodworker's shop is located in the Creative Arts & Technology Center. The club was formed in 2008 to promote community woodworking skills. The complete woodworking machine shop is available to all residents who complete a safety class with "hands-on" training on the safe operation of all machines in the shop. A nominal annual "user fee" is required to replace and sharpen tools and supplies that are used. Residents of every range of skills are encouraged to join, both men and women, as Mentors are available to give you ideas for projects, and help you learn how to do them.
Robson Ranch Stampers create quality greeting cards for all occasions. The cards have unique features – they "POP," slide, move, and sparkle. They delight people of all ages. Gift items made include bookmarks, notepad covers, gift bags, and ornaments. The club is open to new and experienced stampers.
If it has to do with yarn, thread, string or possibly even rope, these club members can do it. They make various items for charity such as knitted and crochet chemo hats, lap robes for wheelchair-bound people, teddy bears, caps for newborns, and other similar projects. They also work on projects for themselves. All levels of skill are welcome, and if you have no skill but want to learn, there's always somebody who will teach you.
Euchre is a social game. Players meet at various houses and have lots of fun, fellowship, food, and some card playing. If you don't know how to play, they will teach you!
The Genealogy Club's goal is to facilitate family history research through programs, education, and sharing research experiences.
The Robson Ranch Inside Straight Poker Club is a fun group for both men and women. They offer Dealer's Choice, Hold'em or Hold'em/Omaha (Hi/Lo) tables as a choice of poker format. Meet new people and enjoy an evening of cards. Betting is low key and cards speak for themselves. Beginners/instruction tables can be arranged if there is a need.
This group shares a love of reading and discusses a variety of books. There are no dues and they welcome all homeowners at Robson Ranch.
This card group plays informal Party Bridge for fun. No partner is needed, open to all skill levels of play.
Mah Jongg is an exciting game played with 152 tiles. A card is used with various combinations for participants to try to win a game.
This club's objective is to actively promote the progressive values of the Democratic Party through networking, discussion groups and community.
They have many interesting and informative programs and speakers for dog owners, fun events and outings twice a year to local dog events and fundraising programs to support organizations that provide rescue services and train dogs to assist physically and mentally challenged owners.
The Red Hat Society is a national organization comprised of purely social clubs just for ladies. They courageously dress up in red hats (un)coordinated with purple outfits, and delight in going out, having fun, making friends, and enjoying life.
The objective of the club is to promote the principles of the Republican Party, promote and encourage good government at all levels, conduct candidate forums and other political activities, and support the Denton County Republican Party. It provides members (and visitors) with the opportunity to meet with elected officials, candidates for public office, and officials at all levels of government, including city, county, school district, state, and federal.
Robson Ranch Roadrunners is a travel club that plans and conducts domestic and international travel for its members in the Robson Ranch community. This includes day and extended day trips and cruises.
This club is a social and service club providing single women and men fellowship and friendship. They are also involved in many community service projects through their Service Committee. To name just a few, Dine Around, Game Nights, Gourmet Groups, Poker Group, Pot Luck Groups, Social Committee, Welcoming Committee, and many more. In addition, they have a Benevolence Committee, BYOB gatherings, and Dallas Cowboy game gatherings. Activities are held once a month.
This committee organizes and plans events/parties for all Robson Ranch homeowners.
The club provides social opportunities and contributes time, talent, and money to charitable organizations for the betterment of the community.
The Robson Rovers RV Club is a club formed by residents of Robson Ranch who have RVs. The purpose of the club is to get together with people who like to RV. The club tries to go on a weekend trip at least once a month and plan other longer trips throughout the year. You must own or rent an RV to belong to the club.
Guests are invited to join in for a fun game day. They play any and all board and card games such as Cribbage, Hand & Foot, Euchre, Rook, Racko, etc., other games such as Dominos, Yahtzee, various dice games, Chess, Checkers, etc., and specialty games such as Business, Sci-fi, Railroad, Historical, Sports, etc.
This is a large group that meets in private homes to play assorted games including Dominoes, cards, parlor games, etc. Each hostess announces through the HOA the location of the current game night. Guests bring their choice of snacks, dessert, wine, coffee, or soft drinks. Open to all Robson Ranch Ladies.
Shutterbugs is a photography club for Robson Ranch residents of all skill levels who enjoy photography and want to continue to learn more. Members are encouraged to expand their horizons with activities that promote fellowship, stimulate the imagination, initiate creativity and learn various processes involved in creating great pictures.
This club consists of a group of retired school personnel (and friends) who support the teachers at Borman Elementary School in Denton by sponsoring two community-wide garage sales a year to earn money so that they may fund grants to the teachers. They have treat days for the teachers as well as soup and salad luncheons.
Any women previously or currently diagnosed with breast cancer are invited to join. They meet monthly to support, encourage, and inform each other. They also participate in the Komen Race for the Cure, the American Cancer Society's Relay for Life, and numerous survivor celebrations and informational forums.
Kiwanis is a global organization of volunteers dedicated to changing the world one child and one community at a time. The principles of serving others in need are reflected in various programs found throughout the community. Come visit a meeting and see the fellowship and commitment of these men and women who are making a difference in our community helping others in need.
>> Charity work enticed these Robson Ranch Texas residents to go for a run.
Support Our Troops, Inc. is a proactive, non-political, non-profit, volunteer, charitable organization that helps provide for the material, physical, and emotional needs of military men and women at home and abroad. They meet and greet troops at DFW Airport, distribute care packages, cards, and letters to service personnel, and provide financial support to various other military charities with a similar mission. Their web site is supportourtroopstexas.com.
The Robson Ranch Veterans' Park is managed and operated by the Robson Ranch Park Committee, which is comprised of Robson Ranch Support Our Troops members. The Park contains bricks honoring Veterans both deceased and alive who are Robson Ranch residents and/or are related to or are friends of residents. Brick drives are conducted in the spring and fall and ceremonies honoring the Veterans are held on Memorial Day and Veterans Day.
At Robson Ranch, rediscover your passion for learning through the Osher Lifelong Learning Institute at the University of North Texas program on Tuesdays and Thursdays at the Clubhouse.
Living in this 55+ community presents many opportunities to participate in a variety of events with neighbors and friends. Homeowners enjoy a social calendar full of activities, annual events and more!
All clubs, classes and organizations are formed and operated by the individual homeowners and are not endorsed or sponsored by the developer or the Homeowners Association. Homeowners are always welcome to form a new club, class or organization if one is not represented here. Information subject to change.
Have questions about Robson Ranch Texas or its models?
Call us at 888-988-3927 or request more info here.


text:
The Treatise on Dragons
Evgueni Tortchinov
Nathan of Gaza "Treatise on the Dragons" presents a very interesting example of the reformation of the Lurianic Kabbalah in the light of the character of the Sabbatean movement and Sabbatai Zevi's personality.
See Gershom Scholem's book Sabbatai Sevi. The Mystical Messiah. pp. 297-325
The original Hebrew text of the "Treatise" can be found in: Be'Iqvoth Mashiah, Ed. by G. Scholem. Jerusalem, 1944 (it is a collection of Nathan of Gaza's works).
Some principal points of Nathan's Kabbalah are:
1. New interpretation of tehiru, or the primordial space of creation which appeared after the contraction (zimzum) of the Light of En-Sof ('Or En-Sof). It contains the remnants of this Light, its traces, or reshimu, some of which counteract the idea of creation (thoughtless lights). These lights are the roots of kelippoth and of all demonic powers of "another side" (sitra ahra). Thus, the process of creation is thought to be the result of the dialectical struggle between two sides, or two aspects of the Absolute itself. The concentration of the reshimu of the thoughtless (i.e.having no thought to create) lights produces the dark world of kelippoth symbolically spoken of as the world of the serpents, or dragons.
2. Reinterpretation of the nature of the Messiah. The roots of Messiah are in the sphere of the highest Light. But En-Sof projects these roots to the world of the srpents because of the circumstance that only Messiah has ability not only to vin the victory over the serpents but to transform them to the abode of holyness. Thus, the spirit of Messiah from the very beginning dvells among the serpents of the kelippoth. He struggles with the kink of the dragons and sometimes this king overcomes the Messiah, torturing him. But at the end Messiah will liberate himself from the shell of kelippoth. he will ascend to this world with the mission of its redemption. But he must again descend into the abyss of the kelippoth to vin the king of the dragons and to change him and all his kingdom into the kingdom of Light.
It will be resulting in the completion of the dialectical process of the mystical purification (catharsis) of the Absolute, and the establishing of the kingdom of God everywhere. And (it is interesting to note) the Messiah himself will become the Holy Serpent (please, remember the Serpent made of silver which was erected by Moses in the desert to save Israelites from the poisonous snakes), or the Holy Dragon, the true King-Pharaoh (the gematria of the word "nahash" -- "serpent"is equal to gematria of the word "mashiah", "Messiah"). There were Gnostic sects (2-3 C.E.) of ophythes and nahasens (both words were derived from the Greek and Aramaic designations of the "serpents") who called the Christ (i.e., Messiah) the Holy Serpent who opened to the spiritualized souls (pnumatics) the mysteries of the Tree of Life. I do not believe in any possible influence of the Gnostic ideas on Nathan of Gaza's thought but the parallels are more than striking (probably, here we meet with the archtypal paradigm in the Jungian sense).
from a post to the DONMEH mail list
Saturday, 28 Nov 1998
Evgueni Tortchinov home page
Nathan of Gaza Sabbatai Zevi Jacob Frank Antinomianism The Sabbatean Movement
page uploaded 9 December 1998

redpajama_set_name: RedPajamaCommonCrawl


text:
Sections Monday January 30th, 2023
Report: Ducey education plan would cost $1B in earnings
Gov. Doug Ducey's proposal to add $2 billion to public education over the next decade through a ballot initiative could cost the state about $1 billion in lost investment earnings, a report released Friday said. The Joint Legislative Budget Committee's analysis of…
Yuma Elementary District 1 to propose increase in property tax levy
Yuma Elementary School District 1 is holding a public hearing Tuesday to notify the community of their intention to levy taxes for Adjacent Ways for the upcoming fiscal year.
PharmCamp in focus: Students eye healthcare fields
A group of 25 middle school students recently had an opportunity to dig deeper into health sciences as part of the University of Arizona's annual PharmCamp.
Camp Verde school system saves 13.4 million gallons of water in single year
Seven years ago the Camp Verde Unified School District installed an Aresenic Remidiation Water System. Between the 2013-2014 school year and the 2014-2015 school year, CVUSD saved 13.4 million gallons of water with the help of upgrades to time clocks,…
Dysart district reveals slashed 2015-16 budget
At Wednesday night's board meeting, the Dysart Unified School District unveiled a proposed $161.3 million operating budget for the 2015-16 school year. But the most notable features were the money that could have been there — and now isn't. The…
Embry-Riddle students to fly in air race
Amelia Earhart is Claire Schineler's idol, so the 20-year-old Embry-Riddle Aeronautical University aeronautical science major and licensed pilot is elated to be flying a single-engine Cessna 172 as part of a four-day, 2,500 nautical mile cross-country air race founded by…
Education notes: Diane Douglas returning for feedback
Arizona Schools Chief Diane Douglas is coming back for another round of feedback with Tucson parents, educators and community members. Douglas, who made her way to Tucson three weeks ago as part of her "We Are Listening" tour, will be in town…
Opinion: That No. 50 ranking? It's built on incomplete data
Everyone gets excited when Arizona is ranked last in something. Those fixated on the recent Census Bureau education report should have found it curious that it shows a decrease in Arizona students between 2012 and 2013. The reason? The Census Bureau only…
Tucson Unified to host teacher fair
The Tucson Unified School District is hosting a teacher fair Friday at Catalina High School, 3645 E. Pima St.
Sanchez makes donations to 2 Tucson Unified schools
Gifts come in the wake of criticism over pay raise, incentive package.
AZ WEEK: English Language Education Gets Court OK
A federal appeals court ruled this week that Arizona's method for teaching English language learners is OK. The decision stemmed from a case filed in 1992 on behalf of children in the Nogales school district. Arizona Week Friday looks at the implications…
Cottonwood's after-school and summer camp program moves to former Boys and Girls Club
The Cottonwood City Council has agreed to allow the Cottonwood Recreation staff to take over operation of the city-owned building that formerly housed the Boys and Girls Club. The building is located at the back of the Old Town Activity…
AZ Ranks Low in Survey of Dad-Friendly States
15 TUCSON, Ariz. - Arizona ranks 42nd in a national survey by state of important factors for working fathers, including health and child-care costs. WalletHub gives Arizona low ratings for economic and social well-being, and says the state has the highest number…
AG probes whether public ed funds paid for abortion
State authorities have launched a criminal investigation into allegations public education money was used to pay for an abortion. The Arizona Attorney General's Office confirmed the nature of the investigation to The Arizona Republic but would not release additional details.…
UofA Chabad builds 'home' for students
When Rabbi Yossi and Naomi Winner first moved to Tucson to start Chabad at the University of Arizona in 2005, they hosted Shabbat dinners in their two-bedroom house. By the end of the first year, they had nearly 100 students…
Ducey looks to tear down the border fence for trade, transportation and education
Those focused on building a fence along the Arizona-Mexico border are being left in yesterday's dust as Gov. Doug Ducey hit high notes in his official visit to Mexico this week. The intent of Ducey's visit is to make the…
School letter grades show students' proficiency growth, more A & B schools


text:
NewsBMG United States 23 Apr 2019
US: Latin independent powerhouse DEL Records enters into new global partnership with BMG
Leading Latin independent powerhouse DEL Records has entered into a new long-term global partnership with BMG. Under the new agreement, BMG will serve as the exclusive worldwide publishing administrator for each of DEL's publishing entities DEL Melodies (BMI), DEL World Songs (ASCAP), and DEL New Music (SESAC). BMG has been the publishing administrator of the DEL catalog since 2016.
Founded in 2008 by CEO Angel del Villar, DEL Records focuses on Regional Mexican music, having launched the careers of chart-topping, award-winning artists Gerardo Ortiz, Luis Coronel, Ulices Chaidez y Sus Plebes, and Regulo Caro. Since 2012, the label and artists have been honored with 15 Billboard Latin Music awards.
This year, at the 2019 Billboard Latin Music Awards (April 25), DEL and its artists are nominated for Regional Mexican Artist of the Year, Solo (Gerardo Ortiz); Regional Mexican Artist of the Year, Duo or Group (T3r Elemento); Regional Mexican Airplay Label of the Year, Regional Mexican Airplay Imprint of the Year, Regional Mexican Albums Label of the Year, and Regional Mexican Albums Imprint of the Year.
For the past three consecutive years, 2017-2019, BMG has been named ASCAP Latin Independent Publisher of the Year, in part for its work with DEL World Songs.
Villar said, "My philosophy has always been to lead and create markets. This has been driven by the love for what I do and the fans who connect with it. As we continue to grow and redefine what it means to be a music label in today's age, we look forward to having BMG as our partners as we look to the future."
Luca Scalisi, President, DEL Records, said, "As a record label that moves markets, Del Records has always been a leader in digital optimization, monetization and marketing. This deal speaks to the great history we have had together on that front, as well as the optimism we have about continuing to lead in our genre, further expand the business model and create new opportunities with partners like BMG."
Thomas Scherer, EVP, Repertoire & Marketing, Los Angeles, said, "BMG agradece de todo corazón DEL Records, their artists and writers, and congratulates them on a decade of success! Latin music has always been a global influence on the creative music community and now serves as an inspiration for the global entertainment industry at-large. DEL has always had a vision for their music and this is just the beginning – much more to come!"


text:
Q: Laravel auth emails localisation Laravel uses Illuminate\Auth\Notifications\ResetPassword class to send password reset email. The message is written in english. How do I translate it into another language. Publishing vendor files doesn't copy this class. I can't edit it since it is in vendor files and is not in the vcs repository.

A: The email notification is sent from CanResetPassword trait, you need to override the method responsible for this and provide your own notification class.
User extends Authenticatable
{
    // ...
    public function sendPasswordResetNotification($token)
    {
        $this->notify(new MyResetPasswordNotification($token));
    }
    // ...
}

And create the notification:
MyResetPasswordNotification extends Notification
{
    public $token;

    public function __construct($token)
    {
        $this->token = $token;
    }

    public function via($notifiable)
    {
        return ['mail'];
    }

    public function toMail($notifiable)
    {
        return (new MailMessage)
            ->line(trans('reset_password.first_line'))
            ->action(trans('reset_password.action', ['route' => route('password.reset', $this->token)))
            ->line(trans('reset_password.last_line');
    }
}

Now you just need to provide the translations.

redpajama_set_name: RedPajamaStackExchange