Chemical engineering trabalhos

...chegue à IA via Python/MySQL (uso de LONGTEXT). * Gestão de Tokens e Cotas: Implementar estratégias de Rate Limiting e gerenciamento de Tokens per Minute (TPM) para evitar erros 429 nas APIs do Google Cloud. * Context Window Strategy: Aplicar técnicas de estruturação (XML Tagging/Chunking) para que a IA analise cadeias dominiais complexas em documentos de 100+ páginas sem se perder. * Prompt Engineering de Alta Fidelidade: Refinar instruções de sistema para garantir que a IA mantenha a "Auditoria Sequencial" e não resuma informações críticas. Requisitos Técnicos: * Domínio de Python: Experiência com bibliotecas de manipulação de dados e integra&cc...

...sequencial por fases (jornadas simbólicas); Módulo de ritual com áudio, imagens, textos e gestos simbólicos; Biblioteca de conteúdos restaurativos (frases, cartas, imagens, áudios); Agendamento inteligente de sessão presencial; Painel administrativo com gestão de usuários, fases, frases e métricas vivas. 2. Integração com Agente de IA (etapa 2) Uso de OpenAI (GPT-4) via API, com prompt engineering avançado; IA com memória contextual por usuário (via Airtable ou banco próprio); Agente com persona definida (voz, estilo, linguagem poética); Capacidade de gerar frases, perguntas simbólicas, escuta afetiva; Acompanhamento de fases com inteligên...

...equivalente) Geração automática qualificada de petição trabalhista com dados do cliente, respeitada a legislação e jurisprudência atualizadas, bem como os rígidos padrões de qualidade escritório. Documento final exportado em Word ou PDF Integração de mensagens automáticas no WhatsApp Instruções ou vídeo explicativo do fluxo criado É imprescindível domínio em engenharia de prompts (prompt engineering) para a construção de peças jurídicas automatizadas com GPT-4, com linguagem técnica, precisão textual e estrutura jurídica completa. Este é o primeiro módulo de automaç&a...

structural stability engineering project for shipping containers home looking for someone with specific shipping containers projects experience

EN Project with the intention of reducing the time for creating cutting files and eliminating errors in saving. Aplication Area: Engineering and manufacturing Automation of saving cutting files and manipulation of drawings, 1 - Save cutting files, considering the file type and correct naming. There is a file with several layers categorized in a standard way, these layers should be separated and saved in different files with specific names according to the layer. 2 - Save steel cutting files and possibly make changes/cuts (e.g., Slide). PT Projeto com intenção reduzir tempo de criação de arquivos de corte e eliminar erros no salvamento. Area: Engenharia e manufatura Automatização de salvamento de arquivos de corte e manipulaç...

...كتاب الميكانيكا الهندسية استاتيكا ترجمة قانونية معتمدة مع الحفاظ على النسق العام بحيث تصلح الترجمة للنشر ككتاب ترجمة جزء من كتاب التحليل العددي للمهندسين الموجود في الرابط في الوصف أدناه ترجمة علمية وقانونية معتمدة بحيث يصلح للنشر ككتاب جامعي علما ان الكتاب 655 صفحة, وإذا أحببت ان تأخذ جزء معين من الكتاب بقدر ما يناسب فلا مانع مع ضرورة التنسيق والمحافظة على النسق العام للصفحة اسم الكتاب Engineering Mechanics - Statics المؤلف hibbeler يمكنك تحميل الكتاب من خلال هذا الرابط ,R.C.%20Statitics%2012th%

Olá bintehawa086, eu notei seu perfil e gostaria de lhe oferecer meu projeto. Nós podemos discutir os detalhes pelo chat.

...Corporations like Turner International, HSBC, Verizon and Walmart We help them update and maintain their core applications as well as migrate to new Technologies resulting in annual cost reductions of 20% while doubling Project Team productivity. We are open source and agile by definition Our Mission: Our goal is to achieve excellence in the creation of value through Architecture and Software Engineering. Our Vision: We commit ourselves to the success of projects with our clients, creating and sharing knowledge in a collaborative and professional environment that promotes the development of valuable relationships. Our Values: Passion, Commitment, Team Spirit, Integrity, Flexibility<br />Informática / Software, Capital Federal, De 51 a 200 trabajadores<br /><...

...elaborado e que chame a atenção principalmente de estudantes de engenharia e profissionais da área, sem deixar de ser interessante para os demais públicos. I'm looking for copywriters to a blog that is starting, I need a post or two a week in Civil engineering, architecture, interior designer, etc. The language adopted is Portuguese. The content must be 100% authentic and images used should be free of copyright. The post does not need to be extensive (if OK), but the content should be well prepared and that draws attention mainly engineering students and professionals, while being interesting to other stakeholders....

Si usted puede manejar esto proyecto  <br />solicitar amablemente.<br />Habilidades necesarias: FileMaker, Facebook, Ext GWT, eBay Servicios Web, JSP<br /> 

Details as discussed earlier on with you in the chat. Kindly refer to attached files. "Project deliverables_latest EMP" is for your instructions "EMP report" is the relevant report that you need to refer to "2013 South Road EMP Final" is the report done last year that you can refer to. However your standard of work is expected to be extremely high as compared to what was done last year.

Details as discussed

Empresa de engenharia civil com foco em projetos arquitetonicos, estruturais, eletrico, hidraulico. Civil engineering company focusing on architectural, structural, electrical, hydraulic projects.

Projetos de Arquitetura e Engenharia. Planta baixa, Cortes, Vistas, Fachada, Cobertura, Localização, Elétrica, Hidráulica, Locação para execução do projeto, Fundação, Pilar, Viga, Laje, Alvenaria, Paisagismo, Decoração etc. --//-- Architecture and Engineering projects. Floorplan, Cuts, Pageviews, Facade, Canopy, Location, ElectricalHydraulic, Lease for project execution, Foundation, Pillar, beam, slab, masonry, landscaping, Decorating etc..

...acompanharem seus candidatos durante os mandatos. Em outras palavras, queremos criar uma identidade candidato - eleitor. Para esse site, imaginamos que seria interessante disponibilizá-lo pelo EC2 da AWS, visto que esperamos um grande aumento de demanda nos meses que precedem as eleições. Falando um pouco sobre mim, sou formado em Análise de Sistemas e cursei um e-learning chamado Startup Engineering de Stanford, onde desenvolvi pequenos projetos no free tier da Amazon. Assim, entendo um pouco da tecnologia mas não tenho conhecimentos suficientes para garantir que um projeto importante como esse consiga acompanhar um pico de demanda como esperado. Neste contexto e contando com a sua experiência, gostaria de sua ajuda nesta fase inicial ...

...journal-ready research paper on Explainable AI (XAI) for predicting and interpreting student academic performance. The study must use multiple academic data sources (exams & quizzes, assignments & projects, and class participation records), which I will provide in CSV format. Scope of work: • Clean, preprocess, and align datasets using student IDs and time frames • Perform relevant feature engineering • Build at least one strong predictive model (with optional comparisons) • Apply explainability techniques such as SHAP, LIME, decision trees, or equivalent, with clear justification • Evaluate predictive performance and interpretability • Produce publication-quality visualizations highlighting influential features • Write the full...

...panels—should be addressed so the aesthetic never compromises practicality. References I’m gathering mood boards and precedent images now and will share them as soon as they’re organised, but I’m happy for you to start with your own style explorations first. Deliverables • Concept sketches outlining alternative form directions • Finalised 3D surface model (preferred: STEP or IGES) ready for engineering hand-off • High-quality renderings in at least three colour / material combinations • A concise material-finish chart noting paint codes, texture specs, and suggested suppliers Acceptance criteria The design must fit within a 1300 mm overall length envelope, allow 12 inch wheels, and provide unobstructed battery swap access...

...website and combine them into scalable workwear bundles. This project focuses on catalogue architecture, bundling logic, and long-term scalability, not marketing content. 2. Project Objectives 1. Replicate supplier garment products into WooCommerce 2. Standardise product data across multiple suppliers 3. Create flexible, configurable workwear bundles 4. Enable future supplier expansion without re-engineering 5. Support both direct purchase and quote-based workflows 3. Scope of Work A. Supplier Product Replication The developer will: • Create WooCommerce variable products that mirror supplier items • Each product must include: o Product title o Description (rewritten or lightly adapted where required) o Product imagery (supplier images provided or sourced with permissi...

I need a skilled structural engineer to create design and drawings for a residential building. Key Requirements: - Design and Drawings: Comprehensive structural designs and detailed drawings. - Collaboration: Work closely with me to understand requirements. - Codes and Regulations: Ensure compliance with local building codes. Ideal Skills and Experience: - Degree in Structural Engineering. - Proven experience in residential projects. - Strong knowledge of building codes. - Proficiency in design software (AutoCAD, Revit, etc.). - Excellent communication skills. Please provide a portfolio showcasing relevant work.

...work — Track current research and emerging repositories (Hugging Face, arXiv, GitHub) to spot promising architectures and training techniques. - klaud8 / hrm ai / chat gpt / claude — Spin up controlled experiments in Python using PyTorch/TensorFlow, comparing baseline performance with fine-tuned variants on representative datasets. — Optimise inference speed, memory footprint, and prompt-engineering workflows so models transition smoothly from notebook to production API. — Document findings in concise experiment reports and integrate successful models into our existing CI/CD pipeline. Deliverables 1. A living benchmark report that ranks at least five candidate models per task on accuracy, latency, and cost. 2. Clean, reproducible training scri...

Hi, I am looking for an experienced academic/engineering professional to help refine and finalize my thesis. The core writing is already complete, but I need support to elevate it to a strong engineering/research standard. Scope of work includes: Refining language, clarity, and academic tone Proper formatting (university/thesis standards) Suggesting and improving graphs, tables, charts, and diagrams Recommending mathematical formulations, functions, or algorithms where appropriate Making the thesis look more engineering- and research-oriented, not just descriptive Light structural consistency checks (flow, transitions, figure placement) Important notes: This is NOT ghostwriting — content already exists Preference for someone with engineering / technical ...

I need detailed site layout plans (8-12 plan in total) that adhere to Australian workplace regulatory requirements. These plans are primarily for regulatory OHS compliance. Marked up plans of site attributes will be provided along with existing fire plans to enable a plan meeting OHS law to be prepared. The layouts must clearly indicate: - Chemical storage areas for flammable liquids, and bulk and packaged flammable gases. - Location of emergency equipment. - various site features Ideal attributes - Based in Australia for easy liaison/communication - Sole trader with ABN - Experience in creating compliant site layout plans. - competitive hourly rate - IP Transferred Example finished product provided

...issues or, when necessary, escalate with clear notes. Typical workflow • Monitor inboxes, chat widgets, and social feeds during agreed hours. • Acknowledge and resolve general questions, order status requests, and simple troubleshooting. • Document each interaction in our Zendesk-style ticketing system so the history is always clear. • Flag product bugs or edge-case problems to the engineering queue with concise replication steps. Acceptance criteria • First reply time under 30 minutes during your shift. • Resolution notes logged, tagged, and closed following the provided template. • Customer satisfaction rating maintained at 90 % or higher. If this sounds like the type of collaborative support environment you enjoy, let’s...

I need a qualified engineer to assess my pool's structural integrity. I have concerns about the foundation, as it seems to be shifting or settling. The surface has become bumpy, indicating possible underlying issues. It happended when we got alot of rain and suddenly got problems with pool. Insurance company ...foundation, as it seems to be shifting or settling. The surface has become bumpy, indicating possible underlying issues. It happended when we got alot of rain and suddenly got problems with pool. Insurance company had an engineer we dont agree with and would like second opinion The ideal candidate should have: - Experience with pool structural assessments - Background in civil or structural engineering - Ability to provide a detailed report on findings and recommend ne...

I need a Google Cloud / BigQuery specialist to stand up an end-to-end, webhook-driven data ingestion pipeline running in our production environment. When our external form system fires a webhook, your Cloud Function (or equivalent service) should capture the JSON payload, write the untouched record to a raw BigQuery table, then immediately process it. Th...then immediately process it. The processing step must • parse any nested JSON, • flatten and clean each answer field, • split the results into two purpose-built reporting tables, and • guarantee idempotency through a hashing technique that blocks duplicates. All components have to be secure, version-controlled, and able to scale with traffic spikes. This is strictly a backend/data-engineering job&mda...

...Technical proficiency and deep commercial in consumer-electronics are a must. Requirements: Significant (> 10 years) experience in design and implementation of small-scale actuation, especially VCM design for small spaces. Deep technical background. You yourself must have designed high-performance actuators. That means most likely an engineering background. If you have an applied math or computer science background, then it must be complemented by engineering application experience. You must have prior commercial experience, e.g. at a tier-1 consumer electronics company. Please Send: If the below is not included, we won’t have enough information to consider your submission: - Resume (education and prior work experience). - Either images of an example V...

I need plans for a flood-proof deck to place a container home on. The deck needs to be: - 7 feet deep concrete - 40 x 40 in size Ideal Skills & Experience: - Experience with structural engineering and flood-resistant designs - Proficiency in concrete work - Knowledge of deck construction

...sketched my backyard cabana by hand and now need it turned into a clean, permit-ready drawing package. The job covers three parts that must come together seamlessly: redrafting my sketches into clear architectural sheets, developing full MEP plans, and completing the engineering calculations that the city will ask for at submission. Here is what I expect back from you: • Architectural sheets: redrawn from my hand sketches, fully dimensioned, properly labeled, and laid out on title blocks ready for printing. • MEP plans • Engineering calculations • A single PDF set plus individual CAD files, all formatted to current California code standards and ready to upload to the city’s permit portal. Accuracy and readability are critical, knowledge and a...

I have two signed Android APKs that share the same brand: a Chinese-language build that already handles user registration smoothly, and an English-language build that currently lacks this flow. My goal is to extract every user-management API call from the Chinese APK—endpoints, headers, payload structures, encryption or signing logic—and transplant that functionality into the English APK so both variants register users in exactly the same way. What I can provide: • The release APKs for both language versions • Valid test accounts and server access for live registration checks • Any additional assets the Chinese build relies on (native libraries, certificates, config files) What I need from you: • Decompile, inspect and document the Chinese APK (jadx, a...

I need help building a working prototype of a small interactive toy. The prototype requires: A pop-up mechanism (using solenoids, springs, and/or small motors). Integration with Raspberry Pi or Arduino for control. Wiring/programming to operate the mechanism. A simple phone/web app to trigger the toy remotely. Requirements: Experience with mechanical design and prototyping. Hands-on skills with Raspberry Pi/Arduino electronics. Must show past project work (photos, CAD, or GitHub). Signed NDA. Deliverable: A working physical prototype (not just design files) that demonstrates the pop-up mechanism controlled by Raspberry Pi/Arduino. Budget: Budget will be discussed based on scope and experience. Please provide: What’s your estimated cost? How did you arrive at that numbe...

Mein AI-basierter Telefonagent ist bereits einsatzbereit – allein der letzte Abschnitt des Skripts braucht Feinschliff. Ich möchte, dass der Abschluss und die Call-to-Action künftig freundlicher, lockerer und trotzdem zielorientiert klingen, d...lockeren Ton. • Stelle sicher, dass Übergang, Sprachtempo und Formulierungen für einen Telefon-Agenten geeignet sind (Natural-Language-AI, keine reinen Textchat-Floskeln). • Liefere das Ergebnis als klar strukturierten Prompt-Block, den ich direkt ins System kopieren kann, plus kurze Erläuterung, warum deine Anpassungen wirken. Idealerweise hast du Erfahrung mit Conversational AI, Prompt Engineering und Sales-Scripts. Wenn du schon erfolgreiche Cold-Call-Prompts oder Voice-Bots optimiert hast, um...

I have a completed engineering report in Microsoft Word that now needs a professional layout pass. More than twenty images have to be resized to a uniform dimension and arranged so the “old model / new model” pairs sit neatly side-by-side. Please build clear, standard-format comparison tables where indicated, strip out the watermark, logos and outdated footer notes, and leave every word of the existing text exactly as it is. The document already carries a neutral, technical style and I want to keep that—no new colour palettes or branding guidelines are required. When you finish, the file should feel clean, cohesive and ready for formal submission. Deliverables • A fully formatted Word file (.docx) • A matching, print-ready PDF Acceptance will be base...

The goal is to move from a blank page to a Scopus-indexed journal publication (research paper) and a full university thesis in theoretical Computer Science. Nothing has been drafted yet, so I need end-to-end scholarly support: shaping the research question, developing a rigorous theoretical framework, and writing both the article and the thesis in parallel. Scope My topic sits under Engineering → Computer Science with a purely theoretical approach. I want to identify a publishable problem, build the proofs or formal models, and present the findings in a style that satisfies Scopus journal standards while also conforming to my institution’s thesis guidelines. Key expectations • Early-stage collaboration to refine the research gap, objectives, and hypotheses &b...

...post-production and client promotional use. Maintain and organize audio equipment, cables, and microphones. Collaborate closely with performers, videographer, and the event organizer. Monitor and adjust sound levels in real time to adapt to venue acoustics and size. Ensure all equipment is handled safely and efficiently during setup and teardown. Requirements: Proven experience in live sound engineering and recording for musicians. Strong knowledge of mixing consoles (analog and digital), microphones, DI boxes, and signal flow. Ability to troubleshoot under pressure in live event settings. Excellent ear for detail, tone, and clarity. Knowledge of recording software and techniques for capturing live performances. Reliable, professional, and punctual Team-oriented with ...

I need a qualified engineer to inspect and sign off on residential windows that have been installed. The windows were already installed before photos were taken. The types of windows installed are: - Double-hung - Mullion - Slider door An ideal freelancer should have: - Relevant engineering qualifications - Experience with residential window installations - Ability to provide formal sign-off documentation

I already have complete 3-D CAD files for a novel vaginal pessary and a full set of dimensional and tolerance drawings. What I still need is the bridge from screen to sterile tray: a small run of physical units that match those specs and are safe for first-in-human use. Material The design is intended for medical-grade silicone; I am open to fluorosilicone if it better meets our chemical-resistance requirements. You’ll need to confirm biocompatibility (ISO 10993) and document any additives or colorants you plan to use. Scope of work • Review my CAD and tolerance stack-ups, suggest any refinements that improve moldability without altering the clinical function. • Select or design an appropriate fabrication process (rapid-tool injection molding, LSR casting, or...

...together with our team) • Build a pipeline and develop long-term customer relationships Compensation • Commission-only (no fixed salary) • Commission from the sales price (negotiable for exceptional candidates / large volumes) • Paid after successful order and payment from the customer (standard sales practice) What we provide • Product documentation, technical specs, and support from our engineering team • Pricing structure and sales materials • Fast response for quotations and project sizing • Ability to customize solutions and deliver at scale Ideal candidate • Proven experience selling B2B industrial products, solar components, or PV systems • Existing network in solar industry is a big plus (EPCs, installers, dev...

I need an engineering stamp for commercial building drawings, specifically for structural permit purposes. The primary need for this stamp is code compliance. Requirements: - Must be a licensed engineer. - Specialization in structural engineering. - Ability to verify and ensure code compliance. Ideal Skills and Experience: - Professional engineering license. - Experience with commercial building projects. - Knowledge of local building codes and regulations. Please provide your credentials and relevant experience. Thank you!

...already fixed; what’s missing is the technical depth that a building official will sign off on. Scope • Produce a full permit package—plans, elevations, sections, schedules, notes, code summary, and all relevant details. • Address the hillside conditions with stone retaining walls exactly where the grade demands them. • Coordinate any required structural information: I may have the footer engineering handled locally, so please separate that portion of your fee or flag what your team can provide. Deliverables 1. Stamped-ready PDFs and editable DWGs. 2. A clear revision schedule: first draft, review window, final issue. When you reply, outline your timeline from award to final issue and any milestones you prefer, plus samples of similar h...

...considered. Project Overview- Mechanical lifting and rotating structural platform 30-ton design load, including human occupancy Multi-cylinder hydraulic lift system with synchronization and redundancy considerations Slew drive / turntable rotation system for controlled movement Scope of Work- Technical review and engineering guidance for hydraulic and mechanical systems Load calculations, safety factors, failure modes, and redundancy analysis Coordination with structural engineering and existing project team Support Florida Building Code compliance and AHJ requirements Assistance with permitting, plan review responses, and stamped documentation Team & Timeline- Join an existing multidisciplinary team with two engineers already onboard Project duration: 3–6 ...

...tables into an insightful visual narrative—clear charts, concise commentary, and an executive-style report or interactive dashboard that highlights the key patterns hiding in the numbers. Here is what I need from you: • A clean, well-documented analysis (Python with pandas, seaborn/matplotlib or R tidyverse are fine) that walks through data profiling, outlier handling, and any necessary feature engineering. • Compelling visualizations—think sales trends, category performance, customer behaviour—that can be dropped straight into a slide deck or shared as an interactive report (Tableau, Power BI, or a notebook with embedded visuals). • A short written summary explaining the main take-aways in plain English, suitable for a non-technical stakeho...

Rapid expansion across our U.S. teams means several mid-level vacancies in Technology, Healthcare, and Engineering must be filled without compromising quality or time-to-hire. The assignment covers the full recruiting lifecycle—from crafting job posts and sourcing passive talent with LinkedIn Recruiter or similar tools, to phone screens, interview coordination, reference checks, and offer negotiation. Each hire must clear three checkpoints: verified technical certifications, 3-10 years of relevant experience, and an educational background that meets either licensing or internal standards. I will give clear intake briefs for every opening and direct access to hiring managers so you can move fast. Deliverables • Weekly shortlist of 5–8 vetted, U.S.-based candidates ...

You will be living and have the right to work in the UK. We need a skilled electrician to upgrade and complete several control panels across multiple sites in London a...complete several control panels across multiple sites in London and Southampton so you will be mobile and have your own tool kit. Key tasks include: - Finish wiring control panels to 3-phase pumps - Wire control panels from scratch - Swap out a PLC on-site in Southampton, converting inputs from 0 to 24V - Full testing and commissioning after wiring Ideal skills and experience: - Electrical engineering background - Experience with 3-phase systems and PLCs - Ability to upgrade and wire control panels - Proficient in testing and commissioning electrical systems Please provide relevant experience and a timeline for c...

I need a licensed professional to review and seal structural plans. The review must ensure compliance with local building codes. Key Requirements: - Review structural plans for code compliance - Provide necessary seals and documentation - Must be licensed in relevant jurisdiction Ideal Skills and Experience: - Expertise in local building codes - Experience with struct...professional to review and seal structural plans. The review must ensure compliance with local building codes. Key Requirements: - Review structural plans for code compliance - Provide necessary seals and documentation - Must be licensed in relevant jurisdiction Ideal Skills and Experience: - Expertise in local building codes - Experience with structural plan review - Professional licensing in engineering or ar...

I'm looking for an experienced freelancer to help create a YouTube podcast. Requirements: - Interview-based format - 60+ minute episodes - High-quality video and audio production - Engaging visuals and graphics Ideal Skills: - Video editing - Audio engineering - Graphic design - Experience with YouTube content creation Please provide a portfolio with similar projects.

...calculations, photographs, and findings. Key Requirements: Demonstrable experience with heritage or listed buildings, ideally ecclesiastical or similar structures. Proven expertise in structural analysis and report preparation. Ability to communicate findings clearly in both technical and accessible language. Ideal Qualifications and Experience: Degree (or equivalent) in Structural or Civil Engineering. Chartered Engineer (MIStructE, MICE, or equivalent status preferred). Strong problem-solving and diagnostic abilities. Previous assignments involving historic or church buildings will be highly regarded. Submission Details: Interested engineers or firms are invited to submit: Company profile and relevant experience. Example(s) of similar reports or heritage projects undertaken....

...environments • Collaborate with cross-functional teams including product and engineering • Mentor junior AI engineers and contribute to technical leadership • Conduct research and implement state-of-the-art AI techniques • Ensure data quality, security, and model performance optimization Required Skills & Qualifications: • 10+ years of experience in AI/ML or Software Engineering roles • Strong proficiency in Python and data processing libraries (NumPy, Pandas) • Hands-on experience with TensorFlow, PyTorch, Scikit-learn • Strong understanding of Deep Learning, NLP, Computer Vision • Experience with Model Deployment & MLOps pipelines • Experience working with Cloud platforms (AWS / Azure / GCP) • Strong knowled...

I need an inspection and sign-off on a newly constructed retaining wall. Requirements: - Verify against engineering plans - Ensure compliance with safety standards - Provide official approval Ideal Skills and Experience: - Civil engineering background - Experience with retaining wall inspections - Knowledge of local building codes I need this done ASAP, so prompt availability is crucial.

I need help removing bricks from a structural carport pier. I'm unsure about what to replace the bricks with; possibly some sort of bracing to the steel pole, going to the ground. Requirements: - Bracing for the beam? - Preserving load-bearing capacity is essential Ideal Skills & Experience: - Structural engineering knowledge - Experience with metal bracing - Recommendations for suitable solutions